Question

Historically, the thickness of bolts from a production line have averaged 10.15 mm with a standard deviation of 1.8 mm.
A random sample of 5 bolts are measured.
Assuming the central limit theorem applies, find the probability that the sample mean is less than 9.75 mm.
Your answer can be rounded to four decimal digit accuracy when entered.

Probability is =

Answer 1

Solution :

Given that ,

mean = = 10.15

standard deviation = = 1.8

n = 5

= 10.15

= / n = 1.8 / 5  

P( < 9.75) = P(( - ) / < (9.75 -10.15) / 1.8 / 5  )

= P(z < -0.50)

= 0.3085

Probability is 0.3085