Question

The mean height of adult men is about 175 centimeters (cm) with standard deviation 7 cm. The mean height of adult women is about 160 cm with standard deviation 6 cm.

If a man and a woman are both 166.5 cm tall, which person’s height is more rare with respect to other people of the same sex? How do you know?

8. Public health statistics indicate that 26% of adults in the US smoke cigarettes.

(a) Sketch the sampling distribution model for the proportion of smokers among a randomly selected samples of 50 adults, indi- cating the mean and the standard deviation.

(b) Health officials gather a random sample of 50 US adults. What is the probability that less than 20% of this sample smoke cigarettes?

Answer 1

Question 1)

The mean height of adult men is about 175 centimeters (cm) with standard deviation 7 cm. The mean height of adult women is about 160 cm with standard deviation 6 cm.

If a man and a woman are both 166.5 cm tall, which person’s height is more rare with respect to other people of the same sex? How do you know?

Answer)

For men

Mean = 175

S.d = 7

X = 166.5 cm

We need to find the z score

Closer the z score to the mean, less rare the value

Z = (x - mean)/s.d

Z = (166.5 - 175)/7 = -1.21

For woman

Z = (166.5 - 160)/6 = 1.08

We can see that men's z score is away from mean by 1.21

While a woman's z score is away from.mean by 1.08

So, man's height is more rare as compared to woman's