Unit 4 (Chpt. 5) TEST

Determine whether the following graph can represent a variable with a normal distribution. Explain your reasoning. If the graph appears to represent a normal​ distribution, estimate the mean and standard deviation. (Since I don't have Quizlet+, I can't insert the image of the actual bell-shaped curve (graph); ergo, I pasted the description.) A bell-shaped curve is over a horizontal x-axis labeled from 8 to 23 in increments of 1, and is centered on 20. From left to right, the curve rises at an increasing rate to 17, and then rises at a decreasing rate to a maximum at 20, it falls at an increasing rate to 23, and then falls at a decreasing rate. Could the graph represent a variable with a normal​ distribution? Explain your reasoning. Select the correct choice below​ and, if​ necessary, fill in the answer boxes within your choice. (Type answers as *whole numbers* (*zero* decimal places).) A.) Yes, the graph fulfills the properties of the normal distribution. The mean is approximately *__(1)__* and the standard deviation is about *_(2)_*. B.) No, because the graph is skewed left. C.) No, because the graph is skewed right. D.) No, because the graph crosses the​ x-axis.

Correct Answer(s): A.) Yes, the graph fulfills the properties of the normal distribution. The mean is approximately *20* and the standard deviation is about *3*.

Use the standard normal table to find the​ z-score that corresponds to the given percentile (round answer to *two* decimal places). If the area is not in the​ table, use the entry closest to the area. If the area is halfway between two​ entries, use the​ z-score halfway between the corresponding​ z-scores. If​ convenient, use technology to find the​ z-score. *P₂* *(I didn't copy the Standard Normal Tables because they're too big.)* The​ z-score that corresponds to P₂ is *___*.

Correct Answer: *-2.05*

The mean height of women in a country (ages 20 - 29) is 64.3 inches. A random sample of 70 women in this age group is selected. What is the probability that the mean height for the sample is greater than 65 inches? Assume σ = 2.88. The probability that the mean height for the sample is greater than 65 inches is *_____*. (Round answer to *four* decimal places.)

Correct Answer: *0.0210*

Assume a member is selected at random from the population represented by the graph. Find the probability that the member selected at random is from the shaded area of the graph (round answer to *four* decimal places). Assume the variable x is normally distributed. (Since I don't have Quizlet+, I can't insert the image of the actual graph; ergo, I pasted the description.) A graph titled *"Standardized Test Composite Scores"* has a horizontal x-axis labeled *"Score"* from about 2 to 41, with tick marks at 6, 28, and 33. A normal curve labeled μ = 21.3 [and] σ = 5.5 is centered above the x-axis at 21.3. Two vertical line segments extend from the curve to the x-axis at 28 and 33. The area below the curve and between the two vertical line segments is shaded and labeled 28 < x < 33. The probability that the member selected at random is from the shaded area of the graph is *_____*.

Correct Answer: *0.0949*

About 77% of all female heart transplant patients will survive for at least 3 years. Seventy female heart transplant patients are randomly selected. What is the probability that the sample proportion surviving for at least 3 years will be less than 73%? Assume the sampling distribution of sample proportions is a normal distribution. The mean of the sample proportion is equal to the population proportion and the standard deviation is equal to *√((p × q)/n)*. The probability that the sample proportion surviving for at least 3 years will be less than 73% is *_____*. (Round answer to *four* decimal places.)

Correct Answer: *0.2119* INcorrect Answer: *0.0503*

Find the area of the shaded region under the standard normal curve (round answer to *four* decimal places). (Since I don't have Quizlet+, I can't insert the image of the actual bell-shaped curve (graph); ergo, I pasted the description.) *(I didn't copy the accompanying Standard Normal Table because it's too big.)* A bell-shaped curve is divided into 2 regions by a line from top to bottom on the right side. The region [to the] left of the line is shaded. The z-axis below the line is labeled *z = 0.67*. The area of the shaded region is *_____*.

Correct Answer: *0.2514*

Find the area of the shaded region under the standard normal curve. If​ convenient, use technology to find the area (round answer to *four* decimal places). (Since I don't have Quizlet+, I can't insert the image of the actual normal curve (graph); ergo, I pasted the description.) A normal curve is over a horizontal z-axis and is centered at 0. Vertical line segments extend from the horizontal axis to the curve at -2.08 and 0. The area under the curve between -2.08 and 0 is shaded. The area of the shaded region is *_____*.

Correct Answer: *0.4812*

For the standard normal distribution shown on the​ right (below), find the probability of z occurring in the indicated region (round to *four* decimal places). (Since I don't have Quizlet+, I can't insert the image of the actual normal curve (graph); ergo, I pasted the description.) *(I didn't copy the accompanying Standard Normal Tables because they're too big.)* A normal curve is over a horizontal axis. A vertical line segment extends from the horizontal axis to the curve at 0.76. The area under the curve and to the left of the vertical line segment is shaded. The probability is *_____*.

Correct Answer: *0.7764*

Assume the random variable x is normally distributed with mean μ = 50 and standard deviation σ = 7. Find the indicated probability (round answer to *four* decimal places). *P(x > 43)* P(x > 43) = *_____*

Correct Answer: *0.8413*

Find the indicated area under the standard normal curve (round answer to *four* decimal places). *To the right of z = -1.88* *(I didn't copy the accompanying Standard Normal Tables because they're too big.)* The area to the right of z = -1.88 under the standard normal curve is *_____*.

Correct Answer: *0.9699*

Use the Standard Normal Table or technology to find the​ z-score that corresponds to the following cumulative area (round answer to *three* decimal places). *0.95* The cumulative area corresponds to the​ z-score of *____*.

Correct Answer: *1.645*

What is the total area under the normal​ curve? Choose the correct answer below. A.) It depends on the standard deviation. B.) It depends on the mean. C.) 1 D.) 0.5

Correct Answer: C.) 1

The graph of the waiting time​ (in seconds) at a red light is shown below on the left with its mean and standard deviation. Assume that a sample size of 100 is drawn from the population. Decide which of the graphs labeled (a) - (c) would most closely resemble the sampling distribution of the sample means (type answers as either *integers* or *decimals*). Explain your reasoning. (Since I don't have Quizlet+, I can't insert the images of the actual graphs; ergo, I pasted their descriptions.) *(Original):* A graph has a coordinate system with a horizontal x-axis labeled *Time (in sec.)* from 0 to 50 in increments of 10, and a vertical P(x)-axis labeled *Rel. frequency* from 0 to 0.04 in increments of 0.005. A curve labeled *μ = 17.9* and *σ = 12.8* falls from left to right at an increasing rate from the point (0, 0.036) to the point (44, 0). A dashed vertical line segment extends from the horizontal axis to the curve at 17.9. All coordinates are approximate. A graph labeled *(a)* has a coordinate system with a horizontal x̄-axis labeled *Time (in sec.)* from 0 to 50 in increments of 10, and a vertical P(x̄)-axis labeled *Rel. frequency* from 0 to 0.400 in increments of 0.05. A bell-shaped curve labeled *μ∨x̄ = 17.9* and *σ∨x̄ = 1.28* is over the horizontal axis and is centered on 17.9. A dashed vertical line segment extends from the horizontal axis to the curve at 17.9. A graph labeled *(b)* has a coordinate system with a horizontal x̄-axis labeled *Time (in sec.)* from -40 to 40 in increments of 10, and a vertical P(x̄)-axis labeled *Rel. frequency* from 0 to 0.04 in increments of 0.005. A bell-shaped curve labeled *μ∨x̄ = 1.8* and *σ∨x̄ = 12.8* is over the horizontal axis and is centered on 1.8. A dashed vertical line segment extends from the horizontal axis to the curve at 1.8. A graph labeled *(c)* has a coordinate system with a horizontal x̄-axis labeled *Time (in sec.)* from -20 to 50 in increments of 10, and a vertical P(x̄)-axis labeled *Rel. frequency* from 0 to 0.04 in increments of 0.005. A bell-shaped curve labeled *μ∨x̄ = 17.9* and *σ∨x̄ = 12.8* is over the horizontal axis and is centered on 17.9. A dashed vertical line segment extends from the horizontal axis to the curve at 17.9. Graph *_(1)_* most closely resembles the sampling distribution of the sample​ means, because μ∨x̄ = *__(2)__*, σ∨x̄ = *__(3)__*, and the graph *______(4)______*.

Correct Answers: *(1):* *(c)* *(2):* *17.9* *(3):* *1.28* *(4):* *approximates a normal curve*

In a recent​ year, the total scores for a certain standardized test were normally​ distributed, with a mean of 500 and a standard deviation of 10.4. Answer parts ​1 (a) - 4 (d) below (round all answers to *four* decimal places). *Part 1 (a):* Find the probability that a randomly selected medical student who took the test had a total score that was less than 491. The probability that a randomly selected medical student who took the test had a total score that was less than 491 is *_____*. *Part 2 (b):* Find the probability that a randomly selected medical student who took the test had a total score that was between 496 and 509. The probability that a randomly selected medical student who took the test had a total score that was between 496 and 509 is *_____*. *Part 3 (c):* Find the probability that a randomly selected medical student who took the test had a total score that was more than 524. The probability that a randomly selected medical student who took the test had a total score that was more than 524 is *_____*. *Part 4 (d):* Identify any unusual events. Explain your reasoning. Choose the correct answer below. A.) The event in part (a) is unusual because its probability is less than 0.05. B.) None of the events are unusual because all the probabilities are greater than 0.05. C.) The events in parts (a) and (b) are unusual because their probabilities are less than 0.05. D.) The event in part (c) is unusual because its probability is less than 0.05.

Correct Answers: *Part 1 (a):* *0.1934* *Part 2 (b):* *0.4563* *Part 3 (c):* *0.0105* *Part 4 (d):* D.) The event in part (c) is unusual because its probability is less than 0.05.

In a recent study on world​ happiness, participants were asked to evaluate their current lives on a scale from 0 to​ 10, where 0 represents the worst possible life and 10 represents the best possible life. The responses were normally​ distributed, with a mean of 5.6 and a standard deviation of 2.1. Answer parts ​1 (a) - 4 (d) below. (Round all answers to *four* decimal places.) *Part 1 (a):* Find the probability that a randomly selected study​ participant's response was less than 4. The probability that a randomly selected study​ participant's response was less than 4 is *_____*. *Part 2 (b):* Find the probability that a randomly selected study​ participant's response was between 4 and 6. The probability that a randomly selected study​ participant's response was between 4 and 6 is *_____*. *Part 3 (c):* Find the probability that a randomly selected study​ participant's response was more than 8. The probability that a randomly selected study​ participant's response was more than 8 is *_____*. *Part 4 (d):* Identify any unusual events. Explain your reasoning. Choose the correct answer below. A.) The events in parts (a) and (c) are unusual because their probabilities are less than 0.05. B.) There are no unusual events because all the probabilities are greater than 0.05. C.) The events in parts (a), (b), and (c) are unusual because all of their probabilities are less than 0.05. D.) The event in part (a) is unusual because its probability is less than 0.05.

Correct Answers: *Part 1 (a):* *0.2231* *Part 2 (b):* *0.3525* *Part 3 (c):* *0.1265* *Part 4 (d):* B.) There are no unusual events because all the probabilities are greater than 0.05.

Consider a uniform distribution from a = 4 to b = 22. (Round all answers to *three* decimal places.) *Part 1 (a):* Find the probability that x lies between 6 and 12. *Part 2 (b):* Find the probability that x lies between 8 and 10. *Part 3 (c):* Find the probability that x lies between 5 and 18. *Part 4 (d):* Find the probability that x lies between 9 and 16. *Definition of the Uniform Distribution:* A uniform distribution is a continuous probability distribution for a random variable *x* between two values *a* and *b* *(a < b)*, where *a ≤ x ≤ b*, and all of the values of *x* are equally likely to occur. The probability density function of a uniform distribution is *y = 1/(b − a)* on the interval from *x = a* to *x = b*. For any value of *x* less than *a*, or greater than​ *b*, *y = 0*. For two values *c and d*, where *a ≤ c < d ≤​ b*, the probability that *x* lies between *c and d* is equal to the area under the curve between *c and​ d*, as shown (in this case, described).​ So, the area of the central shaded region equals the probability that *x* lies between *c and d*. (Since I don't have Quizlet+, I can't insert the image of the actual coordinate system (graph); ergo, I pasted the description below.) A coordinate system has a horizontal x-axis labeled from left to right with tick marks for *a, c, d, and b,* and a vertical y-axis labeled with one tick mark for *1/(b - a)*. A solid horizontal line segment at *y = 1/(b - a)* extends from *x = a* to *x = b*. Between the horizontal axis and this line segment, each of the regions between *x = a* and *x = c*, between *x = c* and *x = d*, and between *x = d* and *x = b* is *"shaded"*. The region between *x = c* and *x = d* is shaded differently (by *"differently"*, it means *"red"*) than the regions between *x = a* and *x = c* and between *x = d* and *x = b*. *Part 1 (a):* The probability that x lies between 6 and 12 is *____*. *Part 2 (b):* The probability that x lies between 8 and 20 is *____*. *Part 3 (c):* The probability that x lies between 5 and 18 is *____*. *Part 4 (d):* The probability that x lies between 9 and 16 is *____*.

Correct Answers: *Part 1 (a):* *0.333* *Part 2 (b):* *0.667* *Part 3 (c):* *0.722* *Part 4 (d):* *0.389*

The per capita energy consumption level​ (in kilowatt-hours) in a certain country for a recent year can be approximated by a normal​ distribution, as shown in the figure (round all answers to the *nearest integer* (*zero* decimal places)). (Since I don't have Quizlet+, I can't insert the image of the actual normal curve; ergo, I pasted the description.) *Part 1 (a):* What consumption level represents the 9th percentile? *Part 2 (b):* What consumption level represents the 24th percentile? *Part 3 (c):* What consumption level represents the third quartile? A normal curve labeled *µ = 2,275 kWh* and *σ = 591.2 kWh* is over a horizontal x-axis labeled *Kilowatt-hours* from 275 to 4,275 in increments of 1,000, and is centered on 2,275. *Part 1 (a):* The consumption level that represents the 8th percentile is *____* kilowatt-hours. *Part 2 (b):* The consumption level that represents the 20th percentile is *____* kilowatt-hours. *Part 3 (c):* The consumption level that represents the third quartile is *____* kilowatt-hours.

Correct Answers: *Part 1 (a):* *1,444* *Part 2 (b):* *1,777* *Part 3 (c):* *2,674*

A water footprint is a measure of the appropriation of fresh water. The per capita water footprint​ (in mega​ gallons) in a certain country for a recent year can be approximated by a normal​ distribution, as shown in the figure (round all answers to *two* decimal places). (Since I don't have Quizlet+, I can't insert the image of the actual normal curve; ergo, I pasted the description.) *Part 1 (a):* What water footprint represents the 81st percentile? *Part 2 (b):* What water footprint represents the 29th percentile? *Part 3 (c):* What water footprint represents the third quartile? A normal curve labeled *µ = 1.65 Mgal* and *σ = 2.92 Mgal* is over a horizontal x-axis labeled *Mega gallons* from -6.35 to 9.65 in increments of 4, and is centered on 1.65. *Part 1 (a):* The water footprint that represents the 81st percentile is *___* Mgal. *Part 2 (b):* The water footprint that represents the 29th percentile is *___* Mgal. *Part 3 (c):* The water footprint that represents the third quartile is *___* Mgal.

Correct Answers: *Part 1 (a):* *4.21* *Part 2 (b):* *0.03* *Part 3 (c):* *3.62* INcorrect Answers: *Part 1 (a):* *4.02* *Part 2 (b):* *2.50* *Part 3 (c):* *3.84*

Use the normal distribution to the right (below) to answer the questions. (Since I don't have Quizlet+, I can't insert the image of the actual graph; ergo, I pasted the description.) *Part 1 (a):* What percent of the scores are less than 19? (Round answer to *two* decimal places.) *Part 2 (b):* Out of 1,500 randomly selected scores, about how many would be expected to be greater than 21? (Round answer to the *nearest whole number* (*zero* decimal places).) A graph titled *"Standardized Test Composite Scores"* has a horizontal x-axis labeled *"Score"* from about 1 to 39 with tick marks at 19 and 21. A normal curve labeled *μ = 20.3* [and] *σ = 5.4* is centered above the x-axis at 20.3. A vertical line segment labeled μ extends from the normal curve to the x-axis at 20.3. *Part 1 (a):* The percent of scores that are less than 19 is *____%*. *Part 2 (b):* About *___* scores would be expected to be greater than 21.

Correct Answers: *Part 1 (a):* *40.49%* *Part 2 (b):* *673* INcorrect Answer(s): *Part 1 (a):* *40.4"5"*

In a recent study on world​ happiness, participants were asked to evaluate their current lives on a scale from 0 to​ 10, where 0 represents the worst possible life and 10 represents the best possible life. The mean response was 5.7 with a standard deviation of 2.2. (Round all answers to *two* decimal places.) *Part 1 (a):* What response represents the 93rd percentile? *Part 2 (b):* What response represents the 57th percentile? *Part 3 (c):* What response represents the first quartile? *Part 1 (a):* The response that represents the 93rd percentile is *___*. *Part 2 (b):* The response that represents the 57th percentile is *___*. *Part 3 (c):* The response that represents the first quartile is *___*.

Correct Answers: *Part 1 (a):* *8.95* *Part 2 (b):* *6.09* *Part 3 (c):* *4.22* INcorrect Answers: *Part 1 (a):* *1.48* *Part 2 (b):* *0.18* *Part 3 (c):* *-0.67*

The annual salary for one particular occupation is normally distributed, with a mean of about $138,000 and a standard deviation of about $19,000. Random samples of 29 are drawn from this population, and the mean of each sample is determined. Find the mean and standard deviation of the sampling distribution of these sample means (round all answers to the *nearest integer* (*zero* decimal places), and *DO NOT* include the *$* in the answers). Then, sketch a graph of the sampling distribution. *Part 1:* The mean is μ∨x̄ = *___(1)___*, and the standard deviation is σ∨x̄ = *__(2)__*. *Part 2:* Sketch a graph of the sampling distribution. Choose the correct answer below. (Since I don't have Quizlet+, I can't insert the images of the actual normal curves (graphs); ergo, I pasted their descriptions.) A.) A normal curve is over a horizontal axis labeled *"Mean salary (in dollars)"* from 81,000 to 195,000 in increments of 9,500, and is centered on 138,000. A vertical line segment extends from the horizontal axis to the curve at 138,000. The curve is near the axis at 81,000 and 195,000. B.) A normal curve is over a horizontal axis labeled *"Mean salary (in dollars)"* from 23,626 to 27,626 in increments of 200, and is centered on 25,626. A vertical line segment extends from the horizontal axis to the curve at 25,626. The curve is near the axis at 23,626 and 27,626. C.) A normal curve is over a horizontal axis labeled *"Mean salary (in dollars)"* from 127,000 to 149,000 in increments of 1,000, and is centered on 138,000. A vertical line segment extends from the horizontal axis to the curve at 138,000. The curve is near the axis at 127,000 and 149,000. D.) A normal curve is over a horizontal axis labeled *"Mean salary (in dollars)"* from 14,626 to 36,626 in increments of 1,000, and is centered on 25,626. A vertical line segment extends from the horizontal axis to the curve at 25,626. The curve is near the axis at 14,626 and 36,626.

Correct Answers: *Part 1:* *(1):* *138,000* *(2):* *3,528* *Part 2:* C.) A normal curve is over a horizontal axis labeled *"Mean salary (in dollars)"* from 127,000 to 149,000 in increments of 1,000, and is centered on 138,000. A vertical line segment extends from the horizontal axis to the curve at 138,000. The curve is near the axis at 127,000 and 149,000.

You work for a consumer watchdog publication and are testing the advertising claims of a tire manufacturer. The manufacturer claims that the life spans of the tires are normally​ distributed, with a mean of 40,000 miles and a standard deviation of 3,000 miles. You test 16 tires and get the following life spans. Complete parts 1 & 2 (a) through 5 (c) below. *47,695 42,585 29,817 35,313 33,881 43,249 43,275 36,295 26,001 33,815 37,324 35,272 33,631 37,075 38,415 44,956* *Part 1 (a):* Draw a frequency histogram to display these data. Use five classes. Choose the correct answer below. (Since I don't have Quizlet+, I can't insert the images of the actual frequency histograms; ergo, I pasted their titles, minimums, maximums, and frequencies.) A.) *Title:* *Life spans of tires* *Min.:* 28,170 *Max.:* 45,526 *Frequencies (from left to right):* *3, 2, 6, 2, 3* B.) *Title:* *Life spans of tires* *Min.:* 28,170 *Max.:* 45,526 *Frequencies (from left to right):* *1, 3, 6, 5, 2* C.) *Title:* *Life spans of tires* *Min.:* 28,170 *Max.:* 45,526 *Frequencies (from left to right):* *2, 3, 6, 3, 2* *Part 2 (a):* Is it reasonable to assume that the life spans are normally​ distributed? Why? Choose the correct answer below. A.) No, because the histogram is neither symmetric nor​ bell-shaped. B.) Yes, because the histogram is neither symmetric nor​ bell-shaped. C.) No, because the histogram is symmetric and​ bell-shaped. D.) Yes, because the histogram is symmetric and​ bell-shaped. *Part 3 (b):* Find the mean of your sample. (Round answer to *one* decimal place.) The mean is *______*. *Part 4 (b):* Find the standard deviation of your sample. (Round answer to *one* decimal place.) The standard deviation is *_____*. *Part 5 (c):* Compare the mean and standard deviation of your sample with those in the​ manufacturer's claim. Discuss the differences. Choose the correct answer below. A.) The sample mean is greater than the claimed​ mean, so, on​ average, the tires in the sample lasted for a longer time. The sample standard deviation is greater than the claimed standard​ deviation, so the tires in the sample had a greater variation in life span. B.) The sample mean is less than the claimed​ mean, so, on​ average, the tires in the sample lasted for a shorter time. The sample standard deviation is less than the claimed standard​ deviation, so the tires in the sample had a smaller variation in life span. C.) The sample mean is less than the claimed​ mean, so, on​ average, the tires in the sample lasted for a shorter time. The sample standard deviation is greater than the claimed standard​ deviation, so the tires in the sample had a greater variation in life span.

Correct Answers: *Part 1 (a):* C.) *Title:* *Life spans of tires* *Min.:* 28,170 *Max.:* 45,526 *Frequencies (from left to right):* *2, 3, 6, 3, 2* *Part 2 (a):* D.) Yes, because the histogram is symmetric and​ bell-shaped. *Part 3 (b):* *37,412.4* *Part 4 (b):* *5,755.1* *Part 5 (c):* C.) The sample mean is less than the claimed​ mean, so, on​ average, the tires in the sample lasted for a shorter time. The sample standard deviation is greater than the claimed standard​ deviation, so the tires in the sample had a greater variation in life span.

You are performing a study about weekly per capita milk consumption. A previous study found weekly per capita milk consumption to be normally​ distributed, with a mean of 43.5 fluid ounces and a standard deviation of 10.8 fluid ounces. You randomly sample 30 people and record the weekly milk consumptions shown below. *35 53 27 35 39 47 31 62 38 48 41 22 33 51 40 41 41 45 48 45 37 28 21 42 57 41 45 39 55 38* *Part 1 (a):* Draw a frequency histogram to display these data. Use seven classes. Choose the correct answer below. (Since I don't have Quizlet+, I can't insert the images of the actual histograms; ergo, I pasted their descriptions.) A.) A histogram has a horizontal axis labeled *"Volume"* from 23.5 to 59.5 in increments of 6, and a vertical axis labeled *"Frequency"* from 0 to 11 in increments of 1. The histogram contains vertical bars of width 6, where one vertical bar is centered over each of the horizontal axis tick marks. The heights of the vertical bars are as follows, where the *volume* is listed *first*, and the *height* is listed *second*: *(23.5, 8); (29.5, 6); (35.5, 6); (41.5, 3); (47.5, 3); (53.5, 2); (59.5, 2)*. B.) A histogram has a horizontal axis labeled *"Volume"* from 23.5 to 59.5 in increments of 6, and a vertical axis labeled *"Frequency"* from 0 to 11 in increments of 1. The histogram contains vertical bars of width 6, where one vertical bar is centered over each of the horizontal axis tick marks. The heights of the vertical bars are as follows, where the *volume* is listed *first*, and the *height* is listed *second*: *(23.5, 2); (29.5, 6); (35.5, 3); (41.5, 8); (47.5, 3); (53.5, 6); (59.5, 2)*. C.) A histogram has a horizontal axis labeled *"Volume"* from 23.5 to 59.5 in increments of 6, and a vertical axis labeled *"Frequency"* from 0 to 11 in increments of 1. The histogram contains vertical bars of width 6, where one vertical bar is centered over each of the horizontal axis tick marks. The heights of the vertical bars are as follows, where the *volume* is listed *first*, and the *height* is listed *second*: *(23.5, 2); (29.5, 3); (35.5, 6); (41.5, 8); (47.5, 6); (53.5, 3); (59.5, 2)*. D.) A histogram has a horizontal axis labeled *"Volume"* from 23.5 to 59.5 in increments of 6, and a vertical axis labeled *"Frequency"* from 0 to 11 in increments of 1. The histogram contains vertical bars of width 6, where one vertical bar is centered over each of the horizontal axis tick marks. The heights of the vertical bars are as follows, where the *volume* is listed *first*, and the *height* is listed *second*: *(23.5, 9); (29.5, 8); (35.5, 5); (41.5, 3); (47.5, 5); (53.5, 8); (59.5, 9)*. *Part 2 (a):* Do the consumptions appear to be normally​ distributed? Explain. Choose the correct answer below. A.) No, because the histogram is neither symmetric nor​ bell-shaped. B.) Yes, because the histogram is neither symmetric nor​ bell-shaped. C.) Yes, because the histogram is symmetric and​ bell-shaped. D.) No, because the histogram is symmetric and​ bell-shaped. *Part 3 (b):* Find the mean of your sample (round answer to *one* decimal place). The mean is *___*. *Part 4 (b):* Find the standard deviation of your sample (round answer to *one* decimal place). The standard deviation is *__*. *Part 5 (c):* Compare the mean and standard deviation of your sample with those of the previous study. Discuss the differences. The sample mean is *__(1)__* than the previous​ mean, so, on​ average, consumption from the sample is *__(2)__* than in the previous study. The sample standard deviation is *__(3)__* than the previous standard deviation by *_(4)_*​, so the milk consumption is *__(5)__* spread out in the sample.

Correct Answers: *Part 1 (a):* C.) A histogram has a horizontal axis labeled *"Volume"* from 23.5 to 59.5 in increments of 6, and a vertical axis labeled *"Frequency"* from 0 to 11 in increments of 1. The histogram contains vertical bars of width 6, where one vertical bar is centered over each of the horizontal axis tick marks. The heights of the vertical bars are as follows, where the *volume* is listed *first*, and the *height* is listed *second*: *(23.5, 2); (29.5, 3); (35.5, 6); (41.5, 8); (47.5, 6); (53.5, 3); (59.5, 2)*. *Part 2 (a):* C.) Yes, because the histogram is symmetric and​ bell-shaped. *Part 3 (b):* *40.8* *Part 4 (b):* *9.7* *Part 5 (c):* *(1):* *less* *(2):* *less* *(3):* *less* *(4):* *1.1* *(5):* *less*

Find the probability and interpret the results. If​ convenient, use technology to find the probability. *The population mean annual salary for environmental compliance specialists is about $64,500. A random sample of 45 specialists is drawn from this population. What is the probability that the mean salary of the sample is less than $62,000​? Assume σ = $6,300.* *Part 1:* The probability that the mean salary of the sample is less than $62,000 is *_____*. (Round answer to *four* decimal places.) *Part 2:* Interpret the results. Choose the correct answer below. A.) About 39% of samples of 45 specialists will have a mean salary less than $62,000. This is not an unusual event. B.) Only 39% of samples of 45 specialists will have a mean salary less than $62,000. This is an extremely unusual event. C.) Only 0.39% of samples of 45 specialists will have a mean salary less than $62,000. This is an extremely unusual event. D.) About 0.39% of samples of 45 specialists will have a mean salary less than $62,000. This is an extremely unusual event.

Correct Answers: *Part 1:* *0.0039* *Part 2:* C.) Only 0.39% of samples of 45 specialists will have a mean salary less than $62,000. This is an extremely unusual event.

The population mean and standard deviation are given below. Find the required probability (round answer to *four* decimal places), and determine whether the given sample mean would be considered unusual. *For a sample of n = 61, find the probability of a sample mean being less than 21.6 if μ = 22 and σ = 1.18.* *(I didn't copy the Standard Normal Tables because they're too big.)* *Part 1:* For a sample of n = 61, the probability of a sample mean being less than 21.6 if μ = 22 and σ = 1.18 is *_____*. *Part 2:* Would the given sample mean be considered​ unusual? The sample mean *__(1)__* be considered unusual because it has a probability that is *__(2)__* than 5%.

Correct Answers: *Part 1:* *0.0040* *Part 2:* *(1):* *would* *(2):* *less*

Find the mean and standard error of the mean of the sampling distribution. Then sketch a graph of the sampling distribution. *The prices of photo printers on a website are normally distributed with a mean of $235 and a standard deviation of $64. Random samples of size 22 are drawn from this population and the mean of each sample is determined.* *Part 1:* The mean of the distribution of sample means is *___*. *Part 2:* The standard deviation of the distribution of sample means is *_____*. (Type answer as either an *integer* or a *decimal* rounded to *three* decimal places.) *Part 3:* Sketch a graph of the sampling distribution. Choose the correct answer below. (Since I don't have Quizlet+, I can't insert the images of the actual bell-shaped curves; ergo, I pasted their descriptions.) A.) A bell-shaped curve is over a horizontal x̄-axis labeled *Mean price (in $)* from -3 to 3 in increments of 1, and is centered on 0. B.) A bell-shaped curve is over a horizontal x̄-axis labeled *Mean price (in $)* from 43 to 427 in increments of 64, and is centered on 235. C.) A bell-shaped curve is over a horizontal x̄-axis labeled *Mean price (in $)* from 194.1 to 275.9 in increments of 13.63, and is centered on 235. D.) A bell-shaped curve is over a horizontal x̄-axis labeled *Mean price (in $)* from 232 to 238 in increments of 1, and is centered on 235.

Correct Answers: *Part 1:* *235* *Part 2:* *13.645* *Part 3:* C.) A bell-shaped curve is over a horizontal x̄-axis labeled *Mean price (in $)* from 194.1 to 275.9 in increments of 13.63, and is centered on 235.

The heights of fully grown trees of a specific species are normally​ distributed, with a mean of 71.5 feet and a standard deviation of 6.00 feet. Random samples of size 13 are drawn from the population. Use the central limit theorem to find the mean and standard error (round answer to *two* decimal places) of the sampling distribution. Then sketch a graph of the sampling distribution. *Part 1:* The mean of the sampling distribution is μ∨x̄ = *___*. *Part 2:* The standard error of the sampling distribution is σ∨x̄ = *___*. *Part 3:* Choose the correct graph of the sampling distribution below. (Since I don't have Quizlet+, I can't insert the images of the actual graphs; ergo, I pasted their descriptions.) A.) A normal curve is over a horizontal x̄-axis labeled from 68.2 to 74.8 in increments of 1.7, and is centered on 71.5. A vertical line segment extends from the horizontal axis to the curve at 71.5. B.) A normal curve is over a horizontal x̄-axis labeled from -2 to 2 in increments of 1, and is centered on 0. A vertical line segment extends from the horizontal axis to the curve at 0. C.) A normal curve is over a horizontal x̄-axis labeled from 59.5 to 83.5 in increments of 6, and is centered on 71.5. A vertical line segment extends from the horizontal axis to the curve at 71.5.

Correct Answers: *Part 1:* *71.5* *Part 2:* *1.66* *Part 3:* A.) A normal curve is over a horizontal x̄-axis labeled from 68.2 to 74.8 in increments of 1.7, and is centered on 71.5. A vertical line segment extends from the horizontal axis to the curve at 71.5.

In a large section of a statistics class, the points for the final exam are normally distributed, with a mean of 72 and a standard deviation of 9. Grades are assigned such that the top 10% receive A's, the next 20% received B's, the middle 40% receive C's, the next 20% receive D's, and the bottom 10% receive F's. Find the lowest score on the final exam that would qualify a student for an A, a B, a C, and a D (round all answers *up* to the *nearest integer* (*zero* decimal places)). *(I didn't copy the Standard Normal Tables because they're too big.)* *Part 1:* The lowest score that would qualify a student for an A is *__*. *Part 2:* The lowest score that would qualify a student for a B is *__*. *Part 3:* The lowest score that would qualify a student for a C is *__*. *Part 4:* The lowest score that would qualify a student for a D is *__*.

Correct Answers: *Part 1:* *84* *Part 2:* *77* *Part 3:* *68* *Part 4:* *61* INcorrect Answers: *Part 3:* *67* *Part 4:* *60*

For the following​ situation, find the mean and standard deviation of the population. List all samples​ (with replacement) of the given size from that population and find the mean of each. Find the mean and standard deviation of the sampling distribution and compare them with the mean and standard deviation of the population. (Round all answers to *two* decimal places.) *The scores of three students in a study group on a test are 93, 97, and 91. Use a sample size of 3.* *Part 1:* The mean of the population is *____*. *Part 2:* The standard deviation of the population is *___*. *Part 3:* Identify all samples of size 3 with the correct accompanying means below. A.) 93, 97, 93; x̄ = 94.33 B.) 97, 93, 93; x̄ = 94.33 C.) 97, 97, 91; x̄ = 95 D.) 91, 91, 97; x̄ = 93 E.) 91, 97, 97; x̄ = 95 F.) 91, 97, 93; x̄ = 93.67 G.) 97, 91, 93; x̄ = 93.67 H.) 93, 93, 91; x̄ = 92.33 I.) 91, 91, 91; x̄ = 91 J.) 91, 93, 91; x̄ = 91.67 K.) 93, 93, 93; x̄ = 93 L.) 93, 91, 93; x̄ = 92.33 M.) 97, 93, 97; x̄ = 95.67 N.) 97, 91, 91; x̄ = 93 O.) 93, 93, 97; x̄ = 94.33 P.) 91, 93, 93; x̄ = 92.33 Q.) 91, 91, 93; x̄ = 91.67 R.) 97, 97, 93; x̄ = 95.67 S.) 93, 91, 91; x̄ = 91.67 T.) 97, 93, 91; x̄ = 93.67 U.) 93, 97, 91; x̄ = 93.67 V.) 97, 97, 97; x̄ = 97 W.) 91, 93, 97; x̄ = 93.67 X.) 91, 97, 91; x̄ = 93 Y.) 93, 97, 97; x̄ = 95.67 Z.) 97, 91, 97; x̄ = 95 [.] 93, 91, 97; x̄ = 93.67 *Part 4:* The mean of the sampling distribution is *____*. *Part 5:* The standard deviation of the sampling distribution is *___*. *Part 6:* Choose the correct comparison of the population and sampling distribution below. A.) The means are not equal and the standard deviation of the sampling distribution is larger. B.) The means are equal but the standard deviation of the sampling distribution is smaller. C.) The means and standard deviations are equal. D.) The means are not equal and the standard deviation of the sampling distribution is smaller. E.) The means are equal but the standard deviation of the sampling distribution is larger.

Correct Answers: *Part 1:* *93.67* *Part 2:* *2.49* *Part 3:* A.) 93, 97, 93; x̄ = 94.33 B.) 97, 93, 93; x̄ = 94.33 C.) 97, 97, 91; x̄ = 95 D.) 91, 91, 97; x̄ = 93 E.) 91, 97, 97; x̄ = 95 F.) 91, 97, 93; x̄ = 93.67 G.) 97, 91, 93; x̄ = 93.67 H.) 93, 93, 91; x̄ = 92.33 I.) 91, 91, 91; x̄ = 91 J.) 91, 93, 91; x̄ = 91.67 K.) 93, 93, 93; x̄ = 93 L.) 93, 91, 93; x̄ = 92.33 M.) 97, 93, 97; x̄ = 95.67 N.) 97, 91, 91; x̄ = 93 O.) 93, 93, 97; x̄ = 94.33 P.) 91, 93, 93; x̄ = 92.33 Q.) 91, 91, 93; x̄ = 91.67 R.) 97, 97, 93; x̄ = 95.67 S.) 93, 91, 91; x̄ = 91.67 T.) 97, 93, 91; x̄ = 93.67 U.) 93, 97, 91; x̄ = 93.67 V.) 97, 97, 97; x̄ = 97 W.) 91, 93, 97; x̄ = 93.67 X.) 91, 97, 91; x̄ = 93 Y.) 93, 97, 97; x̄ = 95.67 Z.) 97, 91, 97; x̄ = 95 [.] 93, 91, 97; x̄ = 93.67 *Part 4:* *93.67* *Part 5:* *1.44* *Part 6:* B.) The means are equal but the standard deviation of the sampling distribution is smaller.

5.4.11

got partially correct