Question

Fill in blanks. Suppose that the weights of all men are normally distributed with
mean = 140 lb and standard deviation = 8 lb. According to the Empirical Rule,
a. Approximately 68% of all men have weights between.............. and................... .
b. Approximately 95% of all men have weights between................... and.................. .
c. Approximately............... % of all men have weights between 116 lb and 164 lb.
d. If Mr.L weighs 130 lb, find its z-score z =...............

Answer 1

Solution :

Using Empirical rule,

(a)

P( - 1< X < + 1) = 68%

P(140 - 8 < X < 140 + 8) = 68%

P(132 < X < 148) = 68%

Approximately 68% of all men have weights between 132 and 148

(b)

P( - 2< X < + 2) = 95%

Approximately 95% of all men have weights between 124 and 156

(c)

P( - 3< X < + 3) = 99.7%

Approximately 99.7%% of all men have weights between 116 lb and 164 lb.

(d)

z = (130 - 140) / 8 = -1.25