Question

A population of values has a normal distribution with

μ

=

156.2

μ

=

156.2

and

σ

=

84

σ

=

84

. You intend to draw a random sample of size

n

=

138

n

=

138

.

Find the probability that a single randomly selected value is greater than 168.4.

P(X > 168.4) =

Find the probability that a sample of size

n

=

138

n

=

138

is randomly selected with a mean greater than 168.4.

P(M > 168.4) =

Enter your answers as numbers accurate to 4 decimal places. Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.

Answer 1

a) and

P( X>168.4)

P ( X>168.4 )=P ( X−μ>168.4−156.2 )=P ((X−μ)/σ>(168.4−156.2)/84)

Since Z=(x−μ)/σ and (168.4−156.2)/84=0.15 we have:

P ( X>168.4 )=P ( Z>0.15 )

Use the standard normal table to conclude that:

P (Z>0.15)=0.440

b)

P ( X>168.4 )=P ( X−μ>168.4−156.2 )=P ( (X−μ)/σ>(168.4−156.2)/7.16)

Since Z=(x−μ)/σ and (168.4−156.2)/7.16=1.7 we have:

P ( X>168.4 )=P ( Z>1.7 )

Use the standard normal table to conclude that:

P (Z>1.7)=0.045