Question

A synthetic fiber used in manufacturing carpet has tensile strength that is normally distributed with mean 75.5 psi and standard deviation 3.5 psi. Find the probability that a random sample of n=7 fiber specimens will have a sample mean tensile strength that exceeds 75.8 psi. Round your answer to two decimal places.

Answer 1

Solution :

Given that ,

mean = = 75.5

standard deviation = = 3.5

n = 7

= 75.5 and

= / n = 3.5 / 7 = 1.3229

P( > 75.8) = 1 - P( < 75.8)

= 1 - P(( - ) / < (75.8 - 75.5) / 1.3229)

= 1 - P(z < 0.23)

= 1- 0.591

= 0.409

= 0.41

Probability = 0.41