Question

EASY 100 PTS! THIS IS A TWO PART PROBLEM NOT MULTIPLE CHOICE

The distribution of the number of children per family in the United States is strongly skewed right with a mean of 2.5 children per family and a standard deviation of 1.3 children per family.

a) Without doing any calculations, which event is more likely? Explain.
Event A: Randomly selecting a family from the United States that has 3 or more children.
Event B: Randomly selecting 40 families from the United States and finding an average of 3 or more children.

b) The probability of one of the two events listed in part (a) can be calculated even though the distribution of the population is strongly skewed right. For which event can the probability be calculated? Explain.

c) Calculate the probability of the event that you selected in part (b).

Answer 1

Explanation:

a. as distribution of number of children per family in the United States is strongly skewed right with a mean of 2.5 children per family and a standard deviation of 1.3 children per family, it is likely that a randomly selecting a family from the United States has 3 or more children.

but if the sample size is increased from a family to 40 families, then it is even more likely because a larger size sample is more likely to follow the distribution. so Event B is more likely

b. Event B's probability calculation requires the right skewness and hence cant be done. but Event A, because its a single family, can be done w/ the mean n SD.

Answer 2

Explanation:

a) Which one is more likely? Explain.

Event A: Randomly selecting a family from the United States that has 3 or more children.

Event B: Randomly selecting 40 families from the United States and finding an average of 3 or more children.

Because the distribution is strongly skewed right, it means families are likely to have more than the mean, 2.5 children. So the probability is high that a randomly selected family will have 3 or more children. But the probability is even higher when 40 families are randomly selected because with a sample size of 40, the results are more likely to follow the main distribution than with a sample size of 1.

For b), because Event B has a larger sample size, its probability can be calculated. With a sample size of 1, it cannot be calculated.