Reference no: EM13371520

1. Length of pregnancies

The length of human pregnancies from conception to birth varies according to a distribution that is approximately Normal with mean 266 days and standard deviation 16 days.

a) What percent of pregnancies last fewer than 240 days (that's about 8 months)?

b) What percent of pregnancies last between 240 and 270 days (roughly between 8 and 9 months)?

c) How long do the longest 25% of pregnancies last?

2. deciles of Normal distributions

The deciles of any distribution are the 10^th, 20^th..., 90^th percentiles, respectively.

a) What are the first and last deciles of the standard Normal distribution?

b) The weights of 9-ounce potato chip bags are approximately Normal with mean 9.25 ounces and standard deviation 0.15 ounce. What are the first and last deciles of this distribution?

3. Life Insurance

A life insurance company sells a term insurance policy to a 21-year-old male that pays $100,000 if that insured dies within the next 5 years. The probability that a randomly chosen male will die each year can be found in mortality tables. The company collects a premium of $250 each year as payment for the insurance. The amount X that the company earns on this policy is $250 per year., less the $100,000 that it must pay if the insured dies. The distribution of X is shown below. Fill in the missing probability in the table and calculate the mean earnings mx.

Age at Death (years)

Age of Death
	21	22	23	24	25	>26
Earnings X Probability	($99,750)	($99,550)	($99,250)	($99,000)	($98,750)	$1,250
	0.00183	0.00186	0.00189	0.00191	0.00193	?

4. More about life insurance

It would be quite risky for you to insure the life of a 21-year-old friend under the terms of Exercise 4.151. There is a high probability that your friend would live and you would gain $1,250 in premiums. But if he were to die, you would lose almost $100,000. Explain carefully why selling insurance is not risky for an insurance company that insure many thousands of 21-year-old men?

Age of Death
	21	22	23	24	25	>26
Earnings X Probability	($99,750)	($99,550)	($99,250)	($99,000)	($98,750)	$1,250
	0.00183	0.00186	0.00189	0.00191	0.00193	?

5 Tastes in music (pp.303) 

Musical styles other than rock and pop are becoming more popular. A survey of college students finds that 40% like country music, 30% like gospel music, and 10% like both.

a) What is the conditional probability that a student likes gospel music if we know that he or she likes country music?

b) What is the conditional probability that a student who does not like country music likes gospel music? (A Venn diagram may help you.)