Question

A normal population has mean μ 30 = 31 and standard deviation σ= 7

(a) What proportion of the population is between 15 and 25?

(b) What is the probability that a randomly chosen value will be between 25 and 35?

Round the answers to at least four decimal places.

Answer 1

X~ N( 31, 7)

a) P( 15< X < 25) = P( < < )

= P( -2.28 < z < -0.86 )

= P( z < -0.86) - P( z < -2.28)

= 1- P( z < 0.86) - [1 - P( z < 2.28)]

= P( z < 2.28) - P( z < 0.86)

= 0.98870 - 0.80511

= 0.18359

b)   P( 25< X < 35) = P( < < )

= P( -0.86 < z < 0.57 )

= P( z < 0.51- P( z < 0.86)

= P( z < 0.57)- [1- P( z < 0.86)]

= P( z < 0.57) -1+ P( z < 0.86)

= 0.71566 - 1 + 0.80511

=0.52077