stats2500mun
11-20-2006, 11:23 AM
I have a few questions for an assignment due tomorrow
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.
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.