Question

SKETCH REQUIRED. PLACE ANSWER WITH PROBABILITY NOTATION IN RECTANGE.

1 A machine that produces a major part for an airplane engine is monitored closely. In the past, 10% of the parts produced would be defective. With a 95%probability, what is the sample size that needs to be taken if the desired margin of error is 0.054?

2.

You are given the following data obtained from a sample of 5 observations taken from a population that has a normal distribution. The mean is 78 and the sample standard deviation is 16.54. Develop 98% confidence interval estimate for the mean of the population.

Answer 1

Answer:

1)
n = z (alpha/2) ^2 p (1 - p) / E^2
  
where
  
alpha/2 = 0.025

Using a table/technology,

z (alpha/2) = 1.96

Also,

E = 0.054

p = 10% = 0.1

Thus,   

n = 118.5679

Rounding up,

n = 119

2)

Given              

          Mean = 78

          Standard deviation = 16.54

          n = 5

          98% confidence Interval:

Lower Limit =   78-27.716

Lower Limit = 50.284

Upper Limit = 78+27.716

Upper Limit = 105.713.