Question

a. You run a factory that produces widgets (no, you'll never escape the widgets). Widget diameters are distributed normally, with a mean of 122mm and a standard deviation of 10mm. You take a random sample of 16 widgets off the factory floor.

What is the probability that this sample average is less than 124? Round your answer to three decimal places, eg 0.192.

b.

You run a factory that produces widgets (no, you'll never escape the widgets). Widget diameters are distributed normally, with a mean of 122mm and a standard deviation of 10mm. You take a random sample of 16 widgets off the factory floor.

What is the probability that this sample average is less than 120? Round your answer to three decimal places, eg 0.192.

Answer 1

= 122,  =10, n=16,  

a)

we want to find P(x < 124 )

formula is

z =0.8

P(x < 124) = P(z < 0.8)

now find P(z < 0.8) using normal z table we get

P(z < 0.8) = 0.7881

P(x < 124) = 0.7881

probability that this sample average is less than 124 =  0.788

b)

we want to find P(x < 120 )

formula is

z = -0.8

P(x < 120) = P(z < -0.8)

now find P(z < -0.8) using normal z table we get

P(z < -0.8) = 0.2119

P(x < 120) = 0.2119

probability that this sample average is less than 120 =  0.212