Question

Suppose a batch of metal shafts produced in a manufacturing company have a standard deviation of 1.3 1.3 and a mean diameter of 202 202 inches. If 70 70 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 less than 0.1 0.1 inches? Round your answer to four decimal places.

Answer 1

Solution :

Given that,

mean = = 202

standard deviation = = 1.3

n = 70

=202

₌ / n = 1.3 70 = 0.1554

Differ less than 0.1 = 202 - 0.1 =202.1 , 202 + 0.1 = 201.9

P(   < 0.1 )

P (201.9 < < 202.1 )

P ( 201.9 - 202 / 0.1554 ) < ( - /) < ( 202.1 - 202 / 0.1554 )

P ( - 0.1 / 0.1554 < z < 0.1 / 0.1554 )

P (-0.64 < z < 0.64 )

P ( z < 0.64) - p ( z < -0.64 )

Using z table

= 0.7389 - 0.2611

= 0.4778

Probability =0.4778