Assume that X has a normal distribution, and find the indicated probability.

14) The mean is u = 40.0 and the standard deviation o = 12.0.

Find P(X < 54.0).

A) 0.3409

B) 0.8790

C) 0.4247

D) 0.6443

Find point estimate.

15) A sample of 6 sheets of cardstock is randomly selected and the following thickness are measured in millimeters. Give a point estimate for the population standard deviation. Round your answer to three decimal places.

2.40, 2.41, 2.35. 2.33, 2.34, 2.29

A) 0.045

B) 0.022

C) 2.353

D) 2.824

Find the indicated probability.

16) in a certain college, 33% of the physics majors belong to ethnic minorities. If 10 students

are selected at random from the physics majors, that is the probability that no more than

6 belong to an ethnic minority?

A) 0.0547

B) 0.913

D) 0.9846

C) 0.9815

Solve the problem.

17 The weights of the fish in a certain lake are normally distributed with a mean of 20 lb and

a standard deviation of 12. If 16 fish are randomly selected, what is the probability that

the mean weight will be between 17.6 and 23.6 Ib?

A) 0.0968

B) 0.6730

C) 0.4032

D) 0.3270

Answer the question.

18) A direct mail company wishes to estimate the proportion of people on a large mailing list that will purchase a product. Suppose the true proportion is 0.06. If 373 are sampled, what is the probability that the sample proportion will differ from the population proportion by more than 0.03? Round your answer to four decimal places.

A) 0.9854

B) 0.0918

C) 0.9082

D) 0.0146

19) Using traditional methods, it takes 9.5 hours to receive a basic driving license. A new license training method using Computer Aided Instruction (CAl) has been proposed. A researcher used the technique with 13 students and observed that they had a mean of 9.4 hours with a standard deviation of variance of 3.24. A level of significance of 0.1 will be used to determine if the technique performs differently than the traditional method. Assume the population distribution is approximately normal. State the null and alternative hypotheses.

A) H0 : u = 9.5, Ha : u not equal 9.5

B) H0 : u = 9.1, Ha : u not equal 9.1

C) H0 : u = 8.9, Ha : u not equal 8.9

D) H0: u = 8.2, Ha : u not equal 8.2

Find the value of the chi-square test statistic for the goodness-of-fit test.

20) You wish to test the claim that workplace accidents are distributed on workdays as follows: Monday: 25%, Tuesday: 15%, Wednesday: 15%, Thursday: 15%, Friday: 30%. In a study of 100 workplace accidents, 26 occurred on a Monday, 16 occurred on a Tuesday, 13 occurred on a Wednesday, 16 occurred on a Thursday, and 29 occurred on a Friday. What is the value of the x2 test statistic? The observed frequencies and the expected frequencies are shown below.

Observed Frequency (O) : 26, 16, 13, 16, 29

Expected Frequency (E) : 25, 15, 15, 15, 30

A) X2 = 0.506

B) X2 = 2.667

C) X2 = 0.473

D) X2 = 1.143

Solve the problem and state your answer or circle your answer as required.

21) Consider two independent random samples with the following results:

n1 = 561 n2 = 642

p1 = 0.38 p2 = 0.26

Use this data to find the 98% confidence interval for the true difference between the population proportions.

Step 1: Find the point estimate that should be used in constructing the confidence interval.

Answer:

Step 2: Find the margin of error. Round your answer to six decimal places.

Answer:

Step 3: Construct the 98% confidence interval. Round your answers to three decimal places.

Left endpoint: ____ Right endpoint: ____

Solve the problem and state your answer or circle your answer as required.

22) The dosage of a drug in a particular tablet needs to be precise. It is essential that the tablets contain 51.82 mg of the active ingredient with a variance of 0.02. A random sample of 25 tablets finds that the variance of the active ingredient is 0.0136. Does the data suggest at a = 0.01 that the variance of the drug in the tablets is less than the desired amount? Assume the population is normally distributed.

Step 1: State the null and alternative hypotheses. Round to four decimal places when

necessary.

Answer: H0 ___ Ha___

Step 2: Determine the critical value(s) of the test statistic. If the test is two-tailed, separate the values with a comma. Round your answer to three decimal places.

Answer:

Step 3: Determine the value of the test statistic. Round your answer to three decimal places.

Answer:

Step 4: Make the decision

A) Reject Null Hypothesis

B) Do not reject Null Hypothesis

Step 5: What is the conclusion?

A) There is sufficient evidence to show that the amount of active ingredient has a variance that is less than the desired amount.

B) There is not sufficient evidence to show that the amount of active ingredient has a variance that is less than the desired amount.

Solve the problem and state your answer or circle your answer as required.

23) Give two independent random samples with the following results:

n1 = 8, n2 = 11

x1 = 126, x2 = 93

s1 = 15, s2 = 31

Use this data to find a 99% confidence interval for the true difference between the population means. Assume that population variances are not equal and that the two populations are normally distributed.

Step 1: Find the point estimate that should be used in finding the margin of error.

Answer:

Step 2: Find the margin of error to be used in constructing a 99% confidence interval. Round your answer to six decimal places.

Answer: