Question

Correct Suppose a batch of metal shafts produced in a manufacturing company have a standard deviation of 1.4 and a mean diameter of 212 inches in r 80 shafts are sampled at random from the batch, what is the probability that the mean diameter of the sample shafts would differ from the population mean by greater than 0.1 inches? Round your answer to four decimal places How to enter your answer

Answer 1

for normal distribution z score =(X- $\small \mu$ )/ $\small \sigma$ x
here mean=       v=	212
std deviation   = $\small \sigma$ =	1.400
sample size       =n=	80
std error= $\small \sigma$ x?= $\small \sigma$ / $\small \sqrt{}$ n=	0.1565

probability of with in 0.1 inches of mean:

probability =

P(211.9<X<212.1)

=

P(-0.6389<Z<0.6389)=

0.7385-0.2615=

0.4770

hence probability that mean diameter differ more than 0.1 inches =1-0.4770 =0.5230

(please try 0.5222 or 0.5229 if above comes wrong due to rounding)