Question

In the United States, males between the ages of 40 and 49 eat on average 105.1 g of fat every day with a standard deviation of 4.5 g ("What we eat," 2012). Assume that the amount of fat a person eats is normally distributed.

(a) State the random variable.

(b) Find the probability that a man age 40-49 in the U.S. eats more than 110 g of fat every day.

(c) Find the probability that a man age 40-49 in the U.S. eats less than 93 g of fat every day.

(d) Find the probability that a man age 40-49 in the U.S. eats between 65 g and 100 g of fat every day.

(e) If you found a man age 40-49 in the U.S. who says he eats less than 65 g of fat every day, would you believe him? Why or why not?

(f) What daily fat level do 95% of all men age 40-49 in the U.S. eat less than?

Answer 1

(a) State the random variable..

X: Daily fat consumption of male in US

b)

The following information has been provided:

We need to compute The corresponding z-value needed to be computed is:

Therefore, we get that

c)

We need to compute . The corresponding z-value needed to be computed:

Therefore,

d)

We need to compute . The corresponding z-values needed to be computed are:

Therefore, we get:

e)

We need to compute . The corresponding z-value needed to be computed:

Therefore,

.no, since the probability is 0

f)

We need to compute x such that . The corresponding z-value is 1.645

x = 105.1 = 7.4025

x = 105.1 + 7.4025

x = 112.5025 g

.