Rockwell hardness of pins of a certain type is known to have a mean value of 50

Question

Rockwell hardness of pins of a certain type is known to have a mean value of 50 and a standard deviation of 1.2. (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 11 pins is at least 51? .0062 (b) What is the (approximate) probability that the sample mean hardness for a random sample of 43 pins is at least 51? You may need to use the appropriate table in the Appendix of Tables to answer this question.

Explanation / Answer

Mean = 50
Stdev = 1.2

To find out the test statistic Z we do : Z= X-Mu/ (Sigma/sqrt(n))

a. P(X>=51) = P(Z> (51.5-50) / (1.2/sqrt(11)) = P(Z>4.15) = .00017
b. P(X>=41) = P(Z> (51.5-50) / (1.2/sqrt(43)) = The P-Value is < 0.00001

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