Question

8 It is a fact that 28% of men in the US are six feet or taller. Suppose that 500 US men were chosen at random. Let X be the number of men in the US that are six feet or taller. a) Find the mean and standard deviation for X. it be considered unusual if 130 of the men were six feet or taller? Show calculation.

Answer 1

(a)

BinomialDistribution

n = 500

p = 0.28

q = 1 - p = 0.72

Mean = np = 500 X 0.28 = 140

Standard deviation = $\sqrt{npq}$

= $\sqrt{500\times 0.28\times 0.72}=10.0399$

(b)

P(X > 130):

Z = (X - $\mu$ )/ $\sigma$ = (130 - 140)/10.0399 = - 0.9960

Table of Area Under Stadard Normal Curve gives area = 0.3413

So,

P(X>130) + 0.5 + 0.3413 = 0.8413

So,
Probability of 130 of the men were six feet or taller is only 84.13 %, which isvery much lessthan 95%.

So, It would not be considered unusual if 130 of the men were sixfeet or taller.