Suppose that in Germany the weight of men M is normally dist

Suppose that in Germany, the weight of men (M) is normally distributed with
a mean of 75 kg and a standard deviation of 16 kg, and the weight of woman (W)
is also normally distributed with mean of 55 kg and a standard deviation of 12 kg.
If one German woman and one German man are randomly selected:

a.) What is the probability that the woman weighs less than 62.7 kg?

b.) What is the probability that the man weighs less than 61.7 kg?

c.) What is the probability that the man weighs less than the woman ?

d.) What is the probability that the woman weighs less than the man ?

e.) Suppose a random sample of 30 men and a random sample of 40 women
are drawn from this population. Find the probability that the average
weight of the men is less than the average weight of the women.

Solution

Suppose that in Germany, the weight of men (M) is normally distributed with
a mean of 75 kg and a standard deviation of 16 kg, and the weight of woman (W)
is also normally distributed with mean of 55 kg and a standard deviation of 12 kg.
If one German woman and one German man are randomly selected:

a.) What is the probability that the woman weighs less than 62.7 kg?

Convert woman