Question

Thompson and Thompson is a steel bolts manufacturing company. Their current steel bolts have a mean diameter of 130 millimeters, and a standard deviation of 6 millimeters. If a random sample of 33 steel bolts is selected, what is the probability that the sample mean would be greater than 130.6 millimeters? Round your answer to four decimal places.

Answer 1

Solution :

Given that ,

mean = = 130

standard deviation = = 6

n = 33

=   = 130

= / n = 6 / 33 = 1.044

P( > 130.6) = 1 - P( < 130.6)

= 1 - P[( - ) / < (130.6 - 130) /1.044 ]

= 1 - P(z < 0.57)

Using z table,    

= 1 - 0.7157

= 0.2843