Question

There is a 0.9991 probability that a randomly selected 32​-year-old male lives through the year. A life insurance company charges ​$173 for insuring that the male will live through the year. If the male does not survive the​ year, the policy pays out 100,000 as a death benefit. Complete parts​ (a) through​ (c) below.

a. From the perspective of the 32-year-old ​male, what are the monetary values corresponding to the two events of surviving the year and not​ surviving?The value corresponding to surviving the year is

​$nothing.

The value corresponding to not surviving the year is

​$nothing.

​(Type integers or decimals. Do not​ round.)

b. If the

32-year-old

male purchases the​ policy, what is his expected​ value?The expected value is

​$nothing.

​(Round to the nearest cent as​ needed.)

c. Can the insurance company expect to make a profit from many such​ policies? Why?

▼

Yes, No,because the insurance company expects to make an average profit of

​$nothing on every 32 dash year old male it insures for 1 year.

B Based on a​ poll, 60%of adults believe in reincarnation. Assume that 66 adults are randomly​ selected, and find the indicated probability. Complete parts​ (a) through​ (d) below.

What is the probability that exactly 5 of the selected adults believe in​ reincarnation?

The probability that exactly 5 of the 6 adults believe in reincarnation is nothing

What is the probability that all of the selected adults believe in​ reincarnation?

The probability that all of the selected adults believe in reincarnation is

What is the probability that at least 5 of the selected adults believe in​ reincarnation?

The probability that at least 5 of the selected adults believe in reincarnation is

Answer 1

a.

The value corresponding to surviving the year is -173

The value corresponding to not surviving the year is 100000

b.

expected value = 0.9991 * -173 + (1 - 0.9991) * 100000 = -82.84

c.

Yes,because the insurance company expects to make an average profit of

$82.84 on every 32 year old male it insures for 1 year.

d.

X ~ Binomial(n = 6, p = 0.6)

probability that exactly 5 of the 6 adults believe in reincarnation is

= 0.186624

probability that all of the selected adults believe in reincarnation is

= 0.046656

probability that at least 5 of the selected adults believe in reincarnation is

= 0.186624 + 0.046656

= 0.23328