Question

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 16 pins is at least 51? 

(b) What is the (approximate) probability that the sample mean hardness for a random sample of 45 pins is at least 51? 

Answer 1

mean = μ = 50

standard deviation = = 1.3

a) n = 16

=  μ = 50

= / n = 1.3 / 16 = 0.325

P( 51) = 1 - P( 51)

= 1 - P[( - ) / (51 - 50) / 0.325 ]

= 1 - P(z ≤ 3.08)

Using z table,    

= 1 - 0.9990

= 0.0010

a) n = 45

=  μ = 50

= / n = 1.3 / 45 = 0.194

P( 51) = 1 - P( 51)

= 1 - P[( - ) / (51 - 50) / 0.194 ]

= 1 - P(z ≤ 5.12)

Using z table,    

= 1 - 1

= 0