The number of accidents per week at a hazardous intersection varies with mean 2.2 and standard deviation 1.4. The distribution of this particular variable is very right skewed.(a) Suppose we let (X-bar) be the mean number of accidents per week at the intersection during 9 randomly chosen weeks. What is the probability that (X-bar) is less than 2?(b) Now let X be the mean number of accidents per week at the intersection during a year (52 weeks). What is the probability that X is less than 2?
Answers
Answer:
The probability that sample mean is less than 2 is 0.1423.
Step-by-step explanation:
Let X denote the number of accidents per week at a hazardous intersection.
It is provided that the mean and standard deviation of X are, μ = 2.2 and σ = 1.4.
(a)
According to the Central Limit Theorem if an unknown population is selected with mean μ and standard deviation σ and appropriately huge random samples (n > 30) are selected from this population with replacement, then the distribution of the sample means will be approximately normally.
Then, the mean of the sample means is given by,
\(\mu_{\bar x}=\mu\)
And the standard deviation of the sample means is given by,
\(\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}\)
As the sample size is not large enough, i.e. n = 9 < 30, the Central Limit Theorem cannot be applied to approximate the sampling distribution of the mean number of accidents per week at the intersection.
And since the distribution of X is not specified, the probability cannot be computed.
(b)
In this case, the sample size is large enough, i.e. n = 52 > 30, the Central Limit Theorem can be applied to approximate the sampling distribution of the mean number of accidents per week at the intersection.
Compute the probability that sample mean is less than 2 as follows:
\(P(\bar X<2)=P(\frac{\bar X-\mu_{\bar x}}{\sigma_{\bar x}}<\frac{2-2.2}{1.4/\sqrt{56}})\\\\=P(Z<-1.07)\\\\=0.14231\\\\\approx 0.1423\)
Thus, the probability that sample mean is less than 2 is 0.1423.
Related Questions
Graph the data.
Find and interpret the slope of the line through the points.
Answers
Answer:
-see link below for graph
-slope- 6/270
Step-by-step explanation:
link in comments
simplify the expression 2\3(-4)-(1/6-8/6
Answers
Answer:
1/8
Step-by-step explanation:
Answer:
When you simplify it, you get the answer of 1.
Step-by-step explanation:
Order of operation rules are required that you multiply and divide before you carrying out addition and/or subtraction.
So, simplify 2/3 / (-4) first, obtaining -1/6.
Now, you have -1/6 - 1/6 + 8/6, which combines to 1 or 6/6.
Anyone know this or could help me out?
Answers
- Explanation: opposite sides of a quadrilateral parallelogram are congruent
2. Solve for X and Y
- 8x-8 = 6x+4
x=6
- 7y+2 = 6y + 16
y=14
3. There are 13,792 books in a library. The library is divided into 16 sections with an equal number of books in each section. The following expression can be used to find the exact number of books in each section. 13,792 + 16 What is the exact number of books in each section of the library?
Answers
Answer:
862 books
Step-by-step explanation:
You have to divide
3x+2(x+2)=22-3(2x-5)
Answers
Answer:
x = 3
Step-by-step explanation:
Assuming you are looking for x
3x+2(x+2)=22-3(2x-5)
3x + 2x + 4 = 22 - 6x + 15
3x + 2x + 6x = 22 + 15 - 4
11x = 33
x = 33 : 11
x = 3-----------------------
check
3 x 3 + 2 x (3 + 2) = 22 - 3 x (2 x 3 - 5)
19 = 19
the answer is good
A health club charges a one-time sign-up fee and a monthly membership fee. The
equation y = 28x + 50 represents what the health club charges. Find the rate of
change.
Answers
Answer:
The rate of change is 28.
Step-by-step explanation:
The equation is in slope-intercept form, y = mx + b, where m is the slope, and b is the y-intercept.
The line plots represent data collected on the travel times to school from two groups of 15 students.
A horizontal line starting at 0, with tick marks every two units up to 28. The line is labeled Minutes Traveled. There is one dot above 4,6,14, and 28. There are two dots above 10, 12, 18, and 22. There are three dots above 16. The graph is titled Bus 47 Travel Times.
A horizontal line starting at 0, with tick marks every two units up to 28. The line is labeled Minutes Traveled. There is one dot above 8, 9,18, 20, and 22. There are two dots above 6, 10, 12,14, and 16. The graph is titled Bus 18 Travel Times.
Compare the data and use the correct measure of variability to determine which bus is the most consistent. Explain your answer.
Bus 18, with an IQR of 16
Bus 47, with an IQR of 24
Bus 18, with a range of 16
Bus 47, with a range of 24
Answers
The bus that is the most consistent, given the data collected on travel times to school from two groups of students is C Bus 18, with a range of 10
How to find the consistent bus ?To determine which bus is the most consistent, we should use the interquartile range (IQR) as the measure of variability. The IQR measures the spread of the middle 50% of the data, which makes it less sensitive to outliers compared to the range.
Bus 47:
Median (Q2): 16
Q1: 10
Q3: 22
IQR = Q3 - Q1 = 22 - 10 = 12
Bus 18:
Median (Q2): 12
Q1: 8
Q3: 18
IQR = Q3 - Q1 = 18 - 8 = 10
Bus 18 has a smaller IQR than Bus 47 (10 vs. 12), which means the travel times for Bus 18 are more consistent.
Note: Figures might be different due to options being for different variant but Bus 18 is the most consistent.
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The ratio of boys to girls in a math class is 7:8. Which
statement must be true about this math class?
Answers
You didn't give me answer choices.
There are no statements to pick from. Please write a proper answer.
A school plans to build a wheelchair ramp from the sidewalk to the front entrance of the school. the slope must be 5/32. the entrance to the school is 81cm above the ground. what is the horizontal distance needed for the ramp?
Answers
The horizontal distance needed for the ramp is 518.4 cm to ensure a slope of 5/32 and reach the entrance of the school, which is 81 cm above the ground.
To find the horizontal distance needed for the ramp, we can use the formula:
Horizontal distance = Vertical distance / Slope
Given that the slope must be 5/32 and the entrance to the school is 81 cm above the ground, we can substitute these values into the formula:
Horizontal distance = 81 cm / (5/32)
To divide by a fraction, we can multiply by its reciprocal:
Horizontal distance = 81 cm * (32/5)
Simplifying:
Horizontal distance = (81 cm * 32) / 5
Horizontal distance = 2592 cm / 5
Horizontal distance = 518.4 cm
Therefore, the horizontal distance needed for the ramp is 518.4 cm to ensure a slope of 5/32 and reach the entrance of the school, which is 81 cm above the ground.
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For the following vectors, (a) find the dot product v•w ; (b) find the angle between v and w , (c) state whether the vectors are parallel, octagonal, or neither. V=-3i-4j, w=6i+8j
A- v•w
B-the angle between v and w is theta ^•?
C- the vectors v and w are?
Answers
B) The angle between vectors v and w can be found using the formula: cos(theta) = (v • w) / (||v|| ||w||), where ||v|| and ||w|| are the magnitudes of vectors v and w respectively.
First, we need to find ||v|| and ||w||:
||v|| = sqrt((-3)^2 + (-4)^2) = 5
||w|| = sqrt((6)^2 + (8)^2) = 10
Now, we can substitute in the values to get:
cos(theta) = (-50) / (5 * 10) = -1
theta = arccos(-1) = pi radians or 180 degrees.
Therefore, the angle between vectors v and w is 180 degrees.
C) Two vectors are parallel if their directions are the same, which can be determined by comparing their unit vectors.
The unit vector of v is:
v_hat = v / ||v|| = (-3/5)i + (-4/5)j
The unit vector of w is:
w_hat = w / ||w|| = (6/10)i + (8/10)j = (3/5)i + (4/5)j
We can see that the unit vectors are in opposite directions, which means that the vectors are anti-parallel or opposite. Therefore, the vectors v and w are neither parallel nor orthogonal.
A marketing firm conducts a survey to determine the ages of their survey subjects who like a new health drink.
This is the resulting data from their survey:
49, 63, 78, 22, 41, 39, 75, 61, 63, 65,
58. 37. 45, 52, 81, 75, 78, 72, 68, 59,
72, 85, 63, 61, 75, 39, 41, 48, 59,55
61, 25, 61, 52, 58, 71, 75, 82, 49, 51
The mean age of the subjects who like the new health drink is (type your answer...)
and the median age of the subjects is (type your answer..)
Answers
Answer:
Mean = 59.1, Median = 61
(there might have been a mistake in calculation (a lot of numbers!))
Step-by-step explanation:
The sample size is 40,
Now, the formula for the mean is,
Mean = (sum of the sample values)/(sample size)
so we get,
\(Mean = (49+63+78+22+41+39+75+61+63+65+58+37+45+52+81+75+78+72+68+59+72+85+63+61+75+39+41+48+59+55+61+25+61+52+58+71+75+82+49+51)/40\\Mean = 2364/40\\Mean = 59.1\)
To find the median, we have to sort the list in ascending (or descending)order,
we get the list,
22,25,37,39,39,41,41,45,48,49,
49,51,52, 52,55,58, 58, 59, 59, 61,
61, 61, 61, 63, 63, 63, 65, 68, 71, 72,
72, 75, 75, 75, 75, 78, 78, 81, 82, 85
Now, we have to find the median,
since there are 40 values, we divide by 2 to get, 40/2 = 20
now, to find the median, we takethe average of the values above and below this value,
\(Median = ((n/2+1)th \ value + (n/2)th \ value )/2\\where, \ the\ (n/2)th \ value \ is,\\n/2 = (total \ number \ of \ samples) /2\\n/2=40/2\\(n/2)th = 20\\Hence\ the (n/2)th \ value \ is \ the \ 20th \ value\)
And the (n+1)th value is the 21st value
Now,
The ((n/2)+1)th value is 61 and the nth value is 61, so the median is,
Median = (61+61)/2
Median = 61
thirty-two thousandths as a fraction
Answers
Answer:
32/1000
Step-by-step explanation:
Answer
\(\frac{32}{1000}\)
Step-by-step explanation:
The goal of an experimental research study is which of the following? A. To make an observation to determine the correlation between two variables B. To make an observation without manipulating any variables C. To demonstrate the existence of a cause-and-effect relationship between two variables D. To make an observation to determine the relationship among several variables
Answers
Option c is correct- To demonstrate the existence of a cause-and-effect relationship between two variables.
The goal of experimental research study is different from the goal of non experimental research. The experiment attempts to show the change in one variable due to change in another variable.
The goal of the experimental method is to provide more definitive conclusions about the causal relationships among the variables in a research hypothesis than what is available from correlational research.
To accomplish this goal the an experiment control extraneous variables and manipulate independent variables. The experiment is done by changing one variable by manipulating which causes change in another variable. The researcher must control the research situation.
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I’m seriously stuck Please help in anyway
Answers
Answer:
Step-by-step explanation:
8 over 2
Answer:
Exact Form:
7 √ 53 /53
Decimal Form:
0.96152394
Step-by-step explanation:
A survey of 35 people was conducted to compare their self-reported height to their actual height. The difference between reported height and actual height was calculated. You're testing the claim that the mean difference is greater than 0.7. From the sample, the mean difference was 0.95, with a standard deviation of 0.44. Calculate the test statistic, rounded to two decimal place
Answers
Answer:
The test statistic is t = 3.36.
Step-by-step explanation:
You're testing the claim that the mean difference is greater than 0.7.
At the null hypothesis, we test if the mean difference is of 0.7 or less, that is:
\(H_0: \mu \leq 0.7\)
At the alternate hypothesis, we test if the mean difference is greater than 0.7, that is:
\(H_1: \mu > 0.7\)
The test statistic is:
\(t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}\)
In which X is the sample mean, \(\mu\) is the value tested at the null hypothesis, s is the standard deviation of the sample and n is the size of the sample.
0.7 is tested at the null hypothesis:
This means that \(\mu = 0.7\)
A survey of 35 people was conducted to compare their self-reported height to their actual height.
This means that \(n = 35\)
From the sample, the mean difference was 0.95, with a standard deviation of 0.44.
This means that \(X = 0.95, s = 0.44\)
Calculate the test statistic
\(t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}\)
\(t = \frac{0.95 - 0.7}{\frac{0.44}{\sqrt{35}}}\)
\(t = 3.36\)
The test statistic is t = 3.36.
2.1x10^8 is how many times the value of 4.2x 10^2
Answers
Answer:
500,000
Step-by-step explanation:
(2.1 * 10^8)/(4.2 * 10^2) =
= 2.1/4.2 * 10^8/10^2
= 0.5 * 10^6
= 500,000
The division of 2.1 × 10⁸ and 4.2 × 10² thus the exponent 2.1 × 10⁸ is 500000 times the exponent 4.2 × 10².
What is a number system?The number system is a way to represent or express numbers.
Since the decimal number system employs ten digits from 0 to 9, it has a base of 10.
Any of the multiple sets of symbols and the guidelines for utilizing them to represent numbers are included in the Number System.
As per the given exponents 2.1 × 10⁸
Let's assume 2.1 × 10⁸ is x times 4.2 × 10².
2.1 × 10⁸ = x (4.2 × 10²)
x = 2.1 × 10⁸/4.2 × 10²
x = 500000
Hence "The division of 2.1 × 10⁸ and 4.2 × 10² thus the exponent 2.1 × 10⁸ is 500000 times the exponent 4.2 × 10²".
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The Venn diagram shows the number of customers who have purchased different types of pets from a pet store, where C represents customers who have purchased cats, D represents customers who have purchased dogs, and F represents customers who have purchased fish.
Circles C, D, and F overlap. Circle C contains 15, circle D contains 21, and circle F contains 12. The overlap of C and F contains 2, the overlap of F and D contains 0, and the overlap of D and C contains 3. The overlap of all 3 circles contains 1. Number 14 is outside of the circles.
How many people are in the set C ∩ D?
4
6
36
38
Answers
The number of people in the set C ∩ D (customers who purchased both cats and dogs) is obtained by adding the overlap of D and C (3) with the overlap of all 3 circles (1), resulting in a total of 4 individuals.
The correct answer is 4.
To determine the number of people in the set C ∩ D (customers who have purchased both cats and dogs), we need to analyze the overlapping regions in the Venn diagram.
Given information:
- Circle C (cats): 15
- Circle D (dogs): 21
- Circle F (fish): 12
- Overlap of C and F: 2
- Overlap of F and D: 0
- Overlap of D and C: 3
- Overlap of all 3 circles: 1
- Number outside of circles: 14
To determine the number of people in the set C ∩ D (customers who have purchased both cats and dogs), we need to consider the overlapping region between circles C and D.
From the information given, we know that the overlap of D and C is 3. Additionally, we have the overlap of all 3 circles, which is 1. The overlap of all 3 circles includes the region where customers have purchased cats, dogs, and fish.
To calculate the number of people in the set C ∩ D, we add the overlap of D and C (3) to the overlap of all 3 circles (1). This gives us 3 + 1 = 4.
Therefore, from the options given correct one is 4.
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Answer: 4
Step-by-step explanation:
trust me bro
What is the AREA of the given circle?
62.83 in²
157.08in²
314.16 in²
628.32 in²
Answers
Answer:
314.16 in²
Step-by-step explanation:
Answer:
\(A\) ≈ \(314.16\)
Step-by-step explanation:
\(A=\pi r^2\)
\(A = \pi (10)^2\)
\(A = \pi (100)\)
\(A\) ≈ \(314.16\)
Help.............
..
Answers
The part of the expression which represents the discounted price before tax is x-35.
The given expression is 0.12x+(x-35).
What is an expression?An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.
a) The part of the expression represents the discounted price before tax is x-35
b) The part of the expression represent the amount of sales tax in dollars is 0.12x
Hence, the part of the expression which represents the discounted price before tax is x-35.
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Find the volume for the regular pyramid.
V =
Answers
Answer:
What do you mean by that?
Hey besties answer this question plz what's x + v/y x 2
Answers
Answer:
x+v/2y
Step-by-step explanation:
Move 2 to the left of y
What is the median of the numbers 63,5,0,0,45,2,23,16
Answers
Answer:
10.5
Step-by-step explanation:
63,5,0,0,45,2,23,16
order from smallest to greatest
0, 0, 2, 5, 16, 23, 45, 63
median = center number
(5 + 16) / 2 =10.5
Match each letter to its correct term. Efficiency Unobtainable Impossible Inefficiency Underutilization 1. A 2. B 3. C
Answers
Each letter should be matched to its correct term as follows;
1. A ⇔ Efficiency.
2. B ⇔ Impossible.
3. C ⇔ Inefficiency.
What is a production possibilities curve?In Economics and Mathematics, a production possibilities curve (PPC) can be defined as a type of graph that is typically used for illustrating the maximum and best combinations of two (2) products that can be produced by a producer (manufacturer) in an economy, if they both depend on the following two (2) factors;
Technology is fixed.Resources are fixed.Based on the production possibilities curve shown in the image attached above, we can reasonably infer and logically deduce that each of the letters represent the following terminologies;
A ⇔ Efficiency: it represent points on the production possibilities curve.B ⇔ Impossible: it represent points outside the production possibilities curve.C ⇔ Inefficiency: it represent points on the interior of a production possibilities curve.Read more on production possibilities here: brainly.com/question/26460726
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Find the area of the triangle on the grid below.
Answers
Answer:
31.5 units²
Step-by-step explanation:
Area = ½*base*height
Height of the triangle on the grid = 9 units
Base = 7 units
Area = ½*9*7
Area = ½*63
Area = 63/2
Area = 31.5 units²
Quadrilateral MNPQ is rotated at 90 degrees counterclockwise about the origin and then rotated 270 degrees counterclockwise about the origin
Answers
After the double rotation, the vertices of the quadrilateral MNPQ are transformed to M'', N'', P'', and Q''. The shape of the quadrilateral may have changed, but the order of the vertices remains the same.
When a quadrilateral MNPQ is rotated counterclockwise at 90 degrees about the origin, each vertex undergoes a transformation.
The new positions of the vertices after this rotation can be denoted as M', N', P', and Q'. The order of the vertices remains the same.
Next, when the rotated quadrilateral M'N'P'Q' is further rotated counterclockwise at 270 degrees about the origin, each vertex undergoes another transformation.
The new positions of the vertices after this rotation can be denoted as M'', N'', P'', and Q''. Again, the order of the vertices remains the same.
It's important to note that a 270-degree counterclockwise rotation is equivalent to a 90-degree clockwise rotation.
The result of the double rotation is equivalent to a single clockwise rotation of 90 degrees.
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Zoe‘s graduation picnic cost $94 for the decorations plus an additional $10 for each attendee at Moose how many attendees can there be if Zoe budgets a total of $474 for her graduation picnic
Answers
Answer:
38 attendees.
Step-by-step explanation:
Subtract the cost of the decorations from the total (474 - 94). You are then left with $380 for all the attendees combined. Divide the total cost of attendees by the cost per attendee (380/ 10). You are left with 38 attendees. You can also check this backwards by multiplying 38 attendees by $10 (380), then adding the cost of decorations (94), and end up with the total cost of $474. I hope this helped!
write an absolute value equation representing all numbers x whose distance from 0 is 6 units
Answers
Answer:
Answer:
Step-by-step explanation:
Step-by-step explanation:
A textile fiber manufacturer is investigating a new drapery yarn, which the company claims has a mean thread elongation of 12 kilograms with a standard deviation of 0.5 kilograms. The company wishes to test the hypothesis against using a random sample of specimens. Calculate the P-value if the observed statistic is . Suppose that the distribution of the sample mean is approximately normal.
Answers
Complete question :
A textile fiber manufacturer is investigating a new drapery yarn, which the company claims has a mean thread elongation of 12 kilograms with a standard deviation of 0.5 kilograms. The company wishes to test the hypothesis H0 : μ = 12 against H1 : μ < 12 using a random sample of n = 4 specimens. Calculate the P-value if the observed statistic is xbar = 11.5. Suppose that the distribution of the sample mean is approximately normal.
Answer:
0.02275
Step-by-step explanation:
Given :
Population mean μ = 12
Standard deviation, σ = 0.5
Sample size, n = 4
Observed statistic, xbar = 11.5
H0 : μ = 12
H1 : μ < 12
The test statistic = (xbar - μ) ÷ σ/sqrt(n)
Test statistic =. (11.5 - 12) ÷ 0.5/sqrt(4)
Test statistic = - 0.5 ÷ 0.5/2
Teat statistic = - 0.5 / 0.25 = - 2
Since, it is stated that, distribution is approximately normal ; then we can use the Z distribution and obtain our Pvalue.
We could obtain P value using the Pvalue Z distribution calculator at α = 0.05, 1 - tail
Pvalue = 0.02275
Or
P(x < - 2) = 0.02275 (Z distribution table)
-2 x -4 =
please help
Answers
Answer:
8
Step-by-step explanation:
Two negatives mean you make a positive and 4 x 2 is 8
Answer:
8
Step-by-step explanation:
Negative times negative = positive
Cancel out the negative symbol
Now multiply: 2*4=8
find the measure of minor arc RV
Answers
The measure of the minor arc m∡rv = 111°
What is the explanation for the above response?Recall that according to the principle of angle of intersecting secants, (a-b)/2 = c
Where a = ∡RV
b = ∡SU = 37°:
and c = ∠T (the angle between intersecting secants.
Thus, if (a-b)/2 = c, and b = c = 37 degrees, then we can substitute these values into the equation to get:
(a - 37) / 2 = 37
Multiplying both sides by 2 gives:
a - 37 = 74
Adding 37 to both sides gives:
a = 111
Therefore, a is equal to m∡rv = 111°.
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