Question

A company received a shipment from a supplier. The supplier company said the mean height of a tire is 21 inches and a standard deviation is 3 inches. The company is planning to choose 55 tires at random. What is the sample mean between 20 and 22? How many tires are likely to be taller than 25 iches?

Answer 1

Solution:

Given that,

mean =   = 21 inches

standard deviation =  = 3 inches

n = 55

So,

= 21

=  ( /n) = ( 3 / 55 ) = 0.4045

P ( 20 <   < 22 )

P ( 20 - 21 / 0.4045) < ( - /) < ( 22 - 21 / 0.4045)

P (- 1 /0.4045 < z < 1 / 0.4045 )

P ( - 1 < z < - 1 )

P ( Z < 1 ) - P ( Z < - 1 )

Using z table

= 0.8413 - 0.1587

= 0.6826

Probability = 0.6826

P ( X < 25 )

= 1 - P ( X > 25 )

= 1 - P ( X - /) < ( 25 - 21 / 3)

= 1 - P ( z < 4 / 3 )

= 1 - P ( z < 1.33 )

Using z table

= 1 - 09082

= 0.0918 * 55

= 5.049

Tries are = 5