Minitab help (a number of questions)

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.
Now, before you reply, I would like help on these questions. Im not looking for anyone to answer them, although that would help. I just need to know how to answer them

For a and c :

you need to look at properties of normal variables. You have the mean which is given and the value you are looking for is STANDARD DEVIATION. These are properties of NORMAL VARIABLES. A quick read of the help included with minitab will teach you this if you type in NORMAL in the space.

(b) P(0.56  x  2.33) for μ = 0 and  = 1
(d) P(59  x  74) for μ = 68 and  = 9.

For the above two, you will need to use the commands in minitab - they are much easier them doing it by hand and if i am correct, it consists of no more then 5 commands.

Tell me if you struggle then i will try help you