1. If X is a normal random variable, find the probabilities:

(a) P(x < −1.45) for μ = 0 and = 1

(b) P(0.56 x 2.33) for μ = 0 and = 1

(c) P(x > 77) for μ = 70 and = 10

(d) P(59 x 74) for μ = 68 and = 9.

2. Assume that x is a binomial random variable with n = 100 and p = 0.5. For each of the probability

below, use MINITAB to calculate (i) the exact binomial probability and (ii) the approximation

obtained using the normal distribution. Is the approximation reasonable?

(a) P(x <= 44)

(b) P(51<=x<=66)

(c) P(x=>71)

3. Use MINITAB to generate random samples of size n = 2 from the norm population with mean 100

and standard deviation 10. (Generate 100 rows of data). Compute ¯x for each sample and plot a

frequency histogram for the 100 values of ¯x. Repeat the process for n = 5, 10. Append all graphs to

your report and comment on the sampling distribution of ¯x as the sample size increases.

4. In an effort to maintain internal control on sales, an auditor takes a sample of sales invoices to evaluate

the mean amount listed on the sales invoices for the warehouse in that month. The following data

are the amounts (in dollars) in a random sample of 12 sales invoices that were selected from the

population of sales invoice:

108.98 145.22 111.45 110.59 127.46 105.26

93.32 90.97 131.56 74.71 125.58 135.11

(a) Use MINITAB to construct a 99% confidence interval for the average amount per sales invoice

in the company. Interpret the result.

(b) Suppose the auditor believes the mean amount per sales invoice is $120. Use MINITAB to test

the hypotheses H0 : μ = 120 at = 0.05 versus HA : μ 6= 120 at = 0.05.

i. Report the value of the test statistic from the printout.

ii. Find and interpret the p-value of the test. State you conclusion.