Question

A sample of n=15 observations is drawn from a normal population with μ=1060 and σ=150. Find each of the following:

A. P(X¯>1137)

Probability =

B. P(X¯<982)

Probability =

C. P(X¯>1009)

Probability =

Answer 1

Solution:

Given that,

mean =  = 1060

standard deviation =  = 150

n = 15

So,

= 1060

=  ( /n) = (150 / 15 ) = 38.7298

A ) p (   > 1137 )

= 1 - p (   < 1137 )

= 1 - p ( - /) < (1137 - 1060 / 38.7298)

= 1 - p ( z < - 23 / 38.7298 )

= 1 - p ( z < - 0.59 )

Using z table

= 1 - 0.2776

= 0.7224

Probability = 0.7224,

B ) p (   < 982 )

= p ( - /) < (982 - 1060 / 38.7298)

= p ( z < - 78 / 38.7298 )

= p ( z < - 2.01 )

Using z table

= 0.0222

Probability = 0.0222

C ) p (   > 1009 )

= 1 - p (   < 1009 )

= 1 - p ( - /) < (1009 - 1060 / 38.7298)

= 1 - p ( z < - 51 / 38.7298 )

= 1 - p ( z < - 1.32 )

Using z table

= 1 - 0.0934

= 0.9066

Probability = 0.9066

,