# 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