Question

5. The breaking strength (in lb/in) for a certain type of fabric has mean 104 and standard deviation 15. A random sample of 100 pieces of fabric is drawn. a) What is the probability that the sample mean breaking strength is less than 100 lb/in? b) Find the 70th percentile of the sample mean breaking strength. c) How large a sample size is needed so that the probability is 0.05 that the sample mean is less than 100?  

Answer 1

µ = 104

sd = 15

n = 100

a)

                               

                                = P(Z < -2.67)

                                = 0.0038

b)

or, x = 100 + 0.52 * 1.5

or, x = 100.78 or 101

c)

or, n = 1.645² * 15² / 4²

or, n = 38.1 or 38