Rockwell hardness of pins of a certain type is known to have a mean value of 50 and a standard deviation of 1.3. (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 12 pins is at least 51?

0.0039 is the probability that the sample mean hardness for a random sample of 12 pins is at least 51.

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 50

Standard Deviation, σ = 1.3

Sample size, n = 12

We are given that the distribution of hardness of pins is a bell shaped distribution that is a normal distribution.

Formula:

Standard error due to sampling =

P(sample mean hardness for a random sample of 12 pins is at least 51)

Calculation the value from standard normal z table, we have,  

0.0039 is the probability that the sample mean hardness for a random sample of 12 pins is at least 51.

yep

step-by-step explanation: