Question

The breaking strength of a rivet has a mean value of 9,950 psi and a standard deviation of 496 psi. (a) What is the probability that the sample mean breaking strength for a random sample of 40 rivets is between 9,850 and 10,150? (Round your answer to four decimal places.)

Answer 1

Solution :

Given that ,

mean = = 9950

standard deviation = = 496

P( 9850< x < 10150 ) = P[(9850 - 9950)/496 ) < (x - ) /  < (10150 -9950) /496 ) ]

= P( -0.20< z < 0.40 )

= P(z < 0.40) - P(z < -0.20 )

Using standard normal table

= 0.6554 - 0.4207 = 0.2347

Probability = 0.2347