Question

Thompson and Thompson is a steel bolts manufacturing company. Their current steel bolts have a mean diameter of 139 millimeters, and a variance of 64.

If a random sample of 41 steel bolts is selected, what is the probability that the sample mean would be greater than 140.3 millimeters? Round your answer to four decimal places.

Answer 1

Solution :

Given that,

mean = = 139

2= 64

standard deviation = = 8

n=41

= =139

= / n = 8/ 41 = 1.249

P( > 140.3) = 1 - P( < 140.3)

= 1 - P[( - ) / < (140.3-139) /1.249 ]

= 1 - P(z <1.04 )

Using z table

= 1 - 0.8508

probability= 0.1492