Question

A manufacturer knows that their items have a normally distributed length, with a mean of 19.5 inches, and standard deviation of 1.6 inches.

If 7 items are chosen at random, what is the probability that their mean length is less than 19.9 inches?________________

Round your answer to four decimal places.

Answer 1

Solution :

Given that ,

mean = = 19.5

standard deviation = = 1.6

n = 7

= 19.5

=  / n = 1.6 / 7=0.6047

P( <19.9 ) = P[( - ) / < (19.9 -19.5) / 0.6047]

= P(z <0.66 )

Using z table  

= 0.7454

probability=0.7454