MATH 221N Week 5 MyStatLab Homework

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1.    Find the area of the shaded region. The graph depicts the standard normal distribution with mean 0 and standard deviation 1.

Click to view page1 of the table.3 Click to view page 2 of the table.4

The area of the shaded region is……………..

(Round to four decimal places as needed.)

1: Standard Normal Distribution Table (Page 1)

2: Standard Normal Distribution Table (Page 2)

3: Standard Normal Distribution Table (Page 1)

4: Standard Normal Distribution Table (Page 2)

2.    Find the area of the indicated region under the standard normal curve.

Click here to view page 1 of the standard normal table.7

Click here to view page 2 of the standard normal table.8 

The area between z = 0 and z = 0.6 under the standard normal curve is…………

(Round to four decimal places as needed.)

5: Area under the standard normal distribution to the left of Z (page 1)

6: Area under the standard normal distribution to the left of Z (page 2)

7: Area under the standard normal distribution to the left of Z (page 1)

8: Area under the standard normal distribution to the left of Z (page 2)

3.    Assume the random variable x is normally distributed with mean μ = 86 and standard deviation σ = 4. Find the indicated probability.

P(x < 78)

P(x < 78) =…………….(Round to four decimal places as needed.) 

4.    Assume the random variable x is normally distributed with mean μ = 87 and standard deviation σ = 5. Find the indicated probability.

P(71 < x < 82)

P(71 < x < 82) = …………………. (Round to four decimal places as needed.)

5.    In a survey of a group of men, the heights in the 20-29 age group were normally distributed, with a mean of 68.2 inches and a standard deviation of 4.0 inches. A study participant is randomly selected. Complete parts (a) through (d) below.

(a)  Find the probability that a study participant has a height that is less than 66 inches.

The probability that the study participant selected at random is less than 66 inches tall is…………

(Round to four decimal places as needed.)

(b)  Find the probability that a study participant has a height that is between 66 and 72 inches.

The probability that the study participant selected at random is between 66 and 72 inches tall is………..

(Round to four decimal places as needed.)

(c)  Find the probability that a study participant has a height that is more than 72 inches.

The probability that the study participant selected at random is more than 72 inches tall is…………..

(Round to four decimal places as needed.)

(d)  Identify any unusual events. Explain your reasoning. Choose the correct answer below.

  A. The events in parts (a) and (c) are unusual because its probabilities are less than ……….

  B. The events in parts (a), (b), and (c) are unusual because all of their probabilities are less than ………..

  C. There are no unusual events because all the probabilities are greater than ……….

  D. The event in part (a) is unusual because its probability is less than …………..

6.    The amounts a soft drink machine is designed to dispense for each drink are normally distributed, with a mean of 12 fluid ounces and a standard deviation of 0.3 fluid ounce. A drink is randomly selected. 

(a)        Find the probability that the drink is less than 11.9 fluid ounces.

(b)        Find the probability that the drink is between 11.6 and 11.9 fluid ounces.

(c)        Find the probability that the drink is more than 12.5 fluid ounces. Can this be considered an unusual event? Explain your reasoning.

(a) The probability that the drink is less than 11.9 fluid ounces is………….

(Round to four decimal places as needed.)

(b) The probability that the drink is between 11.6 and 11.9 fluid ounces is…………….

(Round to four decimal places as needed.)

(c) The probability that the drink is more than 12.5 fluid ounces is……………

(Round to four decimal places as needed.)

Is a drink containing more than 12.5 fluid ounces an unusual event? Choose the correct answer below.

   A. No, because the probability that a drink contains more than 12.5 fluid ounces is less than 0.05, this event is not

       unusual.

   B. Yes, because the probability that a drink contains more than 12.5 fluid ounces is less than 0.05, this event is

        unusual.

    C. No, because the probability that a drink contains more than 12.5 fluid ounces is greater than 0.05, this event is

        not unusual.

   D. Yes, because the probability that a drink contains more than 12.5 fluid ounces is greater than 0.05, this event is        

        unusual.

7.    The mean incubation time for a type of fertilized egg kept at 100.3°F is 20 days. Suppose that the incubation times are approximately normally distributed with a standard deviation of 1 day.

(a)        What is the probability that a randomly selected fertilized egg hatches in less than 19 days?

(b)        What is the probability that a randomly selected fertilized egg hatches between 18 and 20 days?

(c)        What is the probability that a randomly selected fertilized egg takes over 21 days to hatch? 

(a) The probability that a randomly selected fertilized egg hatches in less than 19 days is………….

(Round to four decimal places as needed.)

(b) The probability that a randomly selected fertilized egg hatches between 18 and 20 days is………… (Round to four decimal places as needed.)

(c) The probability that a randomly selected fertilized egg takes over 21 days to hatch is…………….

(Round to four decimal places as needed.)

8.    Use the normal distribution of SAT critical reading scores for which the mean is 515 and the standard deviation is………….Assume the variable x is normally distributed.

(a)          What percent of the SAT verbal scores are less than 550?

(b)          If 1000 SAT verbal scores are randomly selected, about how many would you expect to be greater than 525?

(a)        Approximately…………% of the SAT verbal scores are less than 550.

(Round to two decimal places as needed.)

(b)        You would expect that approximately…………. SAT verbal scores would be greater than 525.

(Round to the nearest whole number as needed.)

9.    The time spent (in days) waiting for a heart transplant for people ages 35-49 can be approximiated by the normal distribution, as shown in the figure to the right.

(a)        What waiting time represents the 5th percentile?

(b)        What waiting time represents the third quartile? 

Click to view page 1 of the Standard Normal Table.11

Click to view page 2 of the Standard Normal Table.12

(a)        The waiting time that represents the 5th percentile is ……… days

(Round to the nearest integer as needed.)

(b)        The waiting time that represents the third quartile is ………   days

(Round to the nearest integer as needed.)

9: Standard Normal Table (Page 1)

10: Standard Normal Table (Page 2)

11: Standard Normal Table (Page 1)

12: Standard Normal Table (Page 2)

10.  The time spent (in days) waiting for a kidney transplant for people ages 35-49 can be approximiated by the normal distribution, as shown in the figure to the right.

(a)        What waiting time represents the 95th percentile?

(b)        What waiting time represents the first quartile?

Click to view page 1 of the Standard Normal Table.15

Click to view page 2 of the Standard Normal Table.16

(a)        The waiting time that represents the 95th percentile is………days. (Round to the nearest integer as needed.)

(b)        The waiting time that represents the first quartile is………….days. (Round to the nearest integer as needed.)

13: Standard Normal Table (Page 1)

14: Standard Normal Table (Page 2)

15: Standard Normal Table (Page 1)

16: Standard Normal Table (Page 2)

 

11.  A population has a mean μ = 81 and a standard deviation σ = 28. Find the mean and standard deviation of a sampling distribution of sample means with sample size n = 49. 

μx =……………..(Simplify your answer.)

σx =……………..(Simplify your answer.)

12.  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. Explain your reasoning.

Graph (1)……………most closely resembles the sampling distribution of the sample means, because

μx =…………….., σx =………….., and the graph (2)            ………………..

 (Type an integer or a decimal.)

(1)        (c)

(b)

(a)

(2)        is the same shape as the graph for the original distribution

approximates a normal curve

13.  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 $60,000. A random sample of 36 specialists is drawn from this population. What is the probability that the mean salary of the sample is less than

$57,500? Assume σ = $6,400.

The probability that the mean salary of the sample is less than $57,500 is…………. (Round to four decimal places as needed.)

Interpret the results. Choose the correct answer below.

A. About 0.95% of samples of 36 specialists will have a mean salary less than $57,500. This is not an unusual event.

B. About 95% of samples of 36 specialists will have a mean salary less than $57,500. This is not an unusual event.

C. Only 0.95% of samples of 36 specialists will have a mean salary less than $57,500. This is an unusual event.

D. Only 95% of samples of 36 specialists will have a mean salary less than $57,500. This is an unusual event.

14.  The mean height of women in a country (ages 20 − 29) is 63.8 inches. A random sample of 60 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 = 2.92. 

The probability that the mean height for the sample is greater than 65 inches is…………….. (Round to four decimal places as needed.)

15.  A machine used to fill gallon-sized paint cans is regulated so that the amount of paint dispensed has a mean of 138 ounces and a standard deviation of 0.30 ounce. You randomly select 35 cans and carefully measure the contents. The sample mean of the cans is 137.9 ounces. Does the machine need to be reset? Explain your reasoning.

(1)……………             , it is (2)……………….that you would have randomly sampled 35 cans with a mean equal to

137.9 ounces, because it (3)…………..within the range of a usual event, namely within (4)…………of the mean of the sample means.

 (1)       No

Yes

(2)        very unlikely

likely

(3)        does not lie

lies

(4)        1 standard deviation

2 standard deviations

3 standard deviations

16.  A manufacturer claims that the life span of its tires is 50,000 miles. You work for a consumer protection agency and you are testing these tires. Assume the life spans of the tires are normally distributed. You select 100 tires at random and test them. The mean life span is 49,777 miles. Assume σ = 900. Complete parts (a) through (c).

(a)        Assuming the manufacturer's claim is correct, what is the probability that the mean of the sample is 49,777 miles or less?

…………………….(Round to four decimal places as needed.)

(b)        Using your answer from part (a), what do you think of the manufacturer's claim?

The claim is (1)…………because the sample mean (2)………..be considered unusual since it

(3)………….within the range of a usual event, namely within (4)………..of the mean of the sample means.

(c)        Assuming the manufacturer's claim is true, would it be unusual to have an individual tire with a life span of 49,777 miles? Why or why not?

(9)…………., because 49,777 (10)…………within the range of a usual event, namely within

(11)…………of the mean for an individual tire.

(1)        inaccurate

accurate

(2)        would not

would

(3)        lies

does not lie

(4)        1 standard deviation

2 standard deviations

3 standard deviations

(9)        No

Yes

(10)      lies

does not lie

(11)      1 standard deviation

2 standard deviations

3 standard deviations

School / College / University / Term Date
Institution
Chamberlain College of Nusing
Term / Date

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