Question

Rockwell hardness of pins of a certain type is known to have a mean value of 50 and a standard deviation of 1.1. (Round your answers to four decimal places.) (a) If the distribution is normal, what is the probability that the sample mean hardness for a random sample of 8 pins is at least 51?

Answer 1

Answer: 0.0051

Explanation:

Given: Mean :
`\mu = 50\text{ inch}`

Standard deviation :
`\sigma =1.1\text{ inch}`

Sample size :
`n=8`

The formula to calculate z is given by :-

`z=(x-\mu)/((\sigma)/(√(n)))`

For x= 51

`z=(51-50)/((1.1)/(√(8)))=2.57129738613\approx2.57`

The P Value =
`P(Z>51)=P(z>2.57)=1-P(z<2.57)=1-0.994915=0.005085\approx0.0051`

Hence, the probability that the sample mean hardness for a random sample of 8 pins is at least 51 =0.0051