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 1.4. (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 18 pins is at least 51? 0.00122 (b) What is the (approximate) probability that the sample mean hardness for a random sample of 40 pins is at least 51? 0.00022 X You may need to use the appropriate table in the Appendix of Tables to answer this question.

Explanation / Answer

Mean is 50 and s is 1.4. Stadard error , SE is s/sqrt(N)=1.4/sqrt(40)=0.22. z is given as (x-mean)/SE

P(x>51)=P(z>(51-50)/0.22)=P(z>4.545 ) or 0

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