Question

A manufacturer knows that their items have a normally distributed length, with a mean of 12.2 inches, and standard deviation of 3.7 inches.

If 7 items are chosen at random, what is the probability that their mean length is less than 13.5 inches?

Answer 1

Solution :

Given that,

mean = = 12.2

standard deviation = = 3.7

n = 7

= 12.2

=  / n = 3.7/ 7=1.398

P( <13.5 ) = P[( - ) / < (13.5-12.2) /1.398 ]

= P(z <0.93 )

Using z table  

=0.8238   

probability= 0.8238