Normal distribution: P(X < A) = P(Z < (A - mean)/standard
deviation)
Mean = 53.5 inches
Standard deviation = 6 inches
A) P( height of less than 65 inches) = P(X < 65)
= P(Z < (65 - 53.5)/6)
= P(Z <
1.92)
(z score rounded to 2 decimal places)
= 0.9726
=
0.973
(final answer rounded to three decimal places)
B) P(height of more than 55.2 inches) = P(X > 55.2)
= 1 - P(X < 55.2)
= 1 - P(Z < (55.2 - 53.5)/6)
= 1 - P(Z <
0.28)
(z score rounded to 2 decimal places)
= 1 - 0.6103
= 0.3897
=
0.390
(final answer rounded to three decimal places)
