Question

Rockwell hardness of pins of a certain type is known to have a mean value of 50 and a standard deviation of 1.5. (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

Solution :

Given that,

mean = = 50

standard deviation = = 1.5

n=16

= =50

= / n =1.5 / 16 = 0.375

P( >51 ) = 1 - P( <51 )

= 1 - P[( - ) / < (51-50) / 0.375]

= 1 - P(z <2.67 )

Using z table

= 1 - 0.9962

= 0.0038

probability= 0.0038

(B)

n=45

= =50

= / n =1.5 / 45 = 0.2236

P( >51 ) = 1 - P( <51 )

= 1 - P[( - ) / < (51-50) / 0.2236]

= 1 - P(z <4.47)

Using z table

= 1 - 0

= 1

probability= 1