Handout assignment IIIDue date: 10/6/20161. A bank has determined that the monthly balances of the saving accounts of it...

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A bank has determined that the monthly balances

April 14, 2018

Handout assignment III
Due date: 10/6/2016
1. A bank has determined that the monthly balances of the saving accounts of its customers are
normally distributed with an average balance of $1,200 and standard deviation of 250. If a
sample of 36 customers is selected,
a. What is the probability that the average monthly balances are between $1,255 and $1,275?
b.

What is the probability that the total balance of the saving accounts for the 36 customers is
less than $41,000?

2. Suppose that a random sample of 20 power window mechanisms is taken from a lot supplied to
an auto manufacturer. Each sampled mechanisms is tested by putting it through continuous updown cycles until it fails. Suppose that in the entire lot, the mean time to failure is 4200 cycles
and that the standard deviation 3400. The mean failure time for the sample is recorded.
a. What is the expected value of the sample mean?
b. What is the standard deviation of the sample mean?
c. Would it be reasonable to assume that the distribution of individual failure times should be
roughly normal?
d. Would it be reasonable to assume that the distribution of sample mean should be roughly
normal?
3.

4.

5. An Internet retailer stocks a popular electronic toy at a warehouse. Every week the retailer makes a
decision about how many units of the toy to stock. Suppose that weekly demand for the toy is
approximately normally with mean of 2500 units and standard deviation of 300 units.
a) What is the probability that weekly demand will be between 2255and 2850?
b) If the retailer has 2750 units on hand at the start of the week, what is the probability that weekly
demand will be greater than inventory?
c) If the retailer wants to limit the probability of being out the stock of the electronic toy to no more
than 2.5% in a week, how many units should the warehouse stock.

6. Chapter 4 4.185 (12th Ed) (use MINITAB)










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