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?


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

Answer 1

a)

for normal distribution z score =(X-μ)/σx
mean μ=	50
standard deviation σ=	1.400

sample size       =n=

18

std error=σx̅=σ/√n=

0.3300

probability that the sample mean hardness for a random sample of 18 pins is at least 51 :

probability =P(X>51)=P(Z>(51-50)/0.33)=P(Z>3.03)=1-P(Z<3.03)=1-0.9988=0.0012

b)

sample size       =n=

45

std error=σx̅=σ/√n=

0.2087

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

probability =P(X>51)=P(Z>(51-50)/0.209)=P(Z>4.79)=1-P(Z<4.79)=1-1=0.0000