Question

• Men's heights are normally distributed with u = 71.2499 inches and o = 14.8530 inches • Men's weights are normally distributed with u = 168.5468 pounds and o = 40.0461 pounds • Women's heights are normally distributed with u = 63.7975 inches and o = 9.6149 inches • Women's weights are normally distributed with j = 135.7459 pounds and o = 30.9147 pounds

Answer 1

4)

Let X denote the blood chloride concentration

Mean, $\mu$ = 104

Standard deviation, $\sigma$ = 5

(a) The required probability = P(X < 105)

= P{Z < (105 - 104)/5}

= P(Z < 0.2)

= 0.5793

(b) The required probability = P{|X - $\mu$ | > $\sigma$ }

= P{|Z| > 1} = 0.3174

No, this probability does not depend on the values of $\mu$ and $\sigma$

(c) Corresponding to most extreme 0.1% of chloride concentration values, the z values are -3.10 and 3.10 respectively

The lower extreme value of the chloride concentration =

μ – 3.10 και σ

= 88.7

The higher extreme value = = 119.30

μ+ 3.10 και σ

5)

Let D denote the diameter of the bearing

Mean, $\mu$ = 0.499 inches

Standard deviation, $\sigma$ = 0.002 inches

The required probability = 1 - P(0.496 ≤ D ≤ 0.504)

= 1- P{(0.496 - 0.499)/0.002 ≤ Z ≤ (0.504 - 0.499)/0.002}

= 1 - P(-1.5 ≤ Z ≤ 2.5) = 0.073

Thus, 7.3% of the bearings produced will not be acceptable