# Long probability questions need help

1. Sep 15, 2008

### sinni8

In a series of N = 1000 items the quality control engineer
assumes the proportion pd = 2:5% of defective items.
(a) What is the expected value and the standard deviation of the number of
defective items?

(b) Assume that Nd is a number of defective items. What is the probability
distribution of Nd:?

(c) Write the normal approximation of the probability distribution of Nd:

(d) Approximate the probability of less than 15 defective items with the aid of
the normal approximation of the probability distribution of Nd: What is the
exact probability?

(e) Assume that he observed Nd = 15 defective items. What is the 95% confidence
interval for the proportion of defective items?

(f) With Nd = 40 test the hypothesis H0 : pd = 2:5% against the alternative
Hα : pd > 2:5%:

(g) Suppose he wishes to estimate the proportion of defective items with accuracy
0:5% with 99% confidence. How many items should be taken for test?

2. Sep 15, 2008

Since you deal with percentages and successes, think about the binomial distribution.
What have you done towards answering these?

3. Sep 15, 2008

### HallsofIvy

Staff Emeritus
Perhaps you misunderstand the purpose of this forum. We are not going to answer questions for you. Show us what you have done so that we can see where you need help and offer suggestions.