Question

A population of values has a normal distribution with μ=116.7μ=116.7 and σ=73.3σ=73.3. You intend to draw a random sample of size n=62n=62.

Find the probability that a single randomly selected value is between 129.7 and 145.6.
P(129.7 < X < 145.6) =

Find the probability that a sample of size n=62n=62 is randomly selected with a mean between 129.7 and 145.6.
P(129.7 < M < 145.6) =

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

solution

P(129.7 < X < 145.6) =P[(129.7-116.7) / 73.3< (x - ) / < (145.6-116.7) / 73.3/ )]

= P( 0.177< Z <0.394 )

= P(Z <0.394 ) - P(Z < 0.177)

Using z table   

=0.6532 -0.5702

probability= 0.0830

(B)

n = 62

m = 116.7

m =  / n= 73.3 / 62=9.3091

P(129.7 < M < 145.6) = P[(129.7-116.7) /9.3091 < (M -m ) /  m < (145.6-116.7) / 9.3091)]

= P( 1.396< Z <3.104 )

= P(Z <3.104 ) - P(Z <1.396 )

Using z table

=0.999-0.9186

=0.0804

probability=0.0804