Question

The population of lengths of aluminum-coated steel sheets is normally distributed with a mean of 30.05 inches and a standard deviation of .2 inches.

What is the probability that a randomly selected sample of 4 sheets will have an average length of less than 29.9 inches long?

Answer 1

Answer: 0.0668

Explanation:

Given : The population of lengths of aluminum-coated steel sheets is normally distributed with a mean of 30.05 inches and a standard deviation of 0.2 inches.

i.e.
`\mu=30.5` and
`\sigma=0.2`

Let x denotes the lengths of aluminum-coated steel sheets.

Then the probability that a randomly selected sample of 4 sheets will have an average length of less than 29.9 inches long will be :-

`P(x<29.9)=P((x-\mu)/((\sigma)/(√(n)))<(29.9-30.05)/((0.2)/(√(4))))\\\\=P(z<-1.5)=1-P(z<1.5)\ \ [\because\ P(Z<-z)=1-P(Z<z)]`

`=1-0.9332= 0.0668` [by using the z-value table ]

Hence, the required probability = 0.0668