Answers must be in excel
36) Slot Machine. The author purchased a slot machine configured so that there is a 1/2000 probability of winning the jackpot on any individual trial. Although no one would seriously consider tricking the author, suppose that a guest claims that she played the slot machine 5 times and hit the jackpot twice.
a) find the probability of exactly 2 jackpots in 5 trials
b) find the probability of at least 2 jackpots in 5 trials
c) Does the guest’s claim of hitting 2 jackpots in 5 trials seem valid? Explain.
Gender Selection. In a test of the YSORT method of gender selection, 152 babies are born to couples trying to have baby boys, and 127 of those babies are boys.
a) If the gender selection method has no effect and boys and girls are equally likely, find the mean and standard deviation for the numbers of boys born in groups of 152.
b) Is the result of 127 boys unusual? Does it suggest that the gender-selection method appears to be effective?
Life insurance. There is a 0.9986 probability that a randomly selected 30 year old male lives through the year. A Fidelity life insurance company charges $161 for insuring that the male lives through the year . If the male does not survive throughout the year, the policy pays out $100,000 as a death benefit. Assume that the company sells 1300 such policies to 30 year old males, so it collects $209,300 in policy payments. The company will make a profit if the number of deaths in the group is two or fewer.
a) What is the mean number of deaths in such groups of 1300 males?
b) Use the Poisson distribution to find the probability that the company makes a profit from the 1300 policies.
c) Use the binomial distribution to find the probability that the company makes a profit from the 1300 policies, then compare the result to the result found in question (b).
10) Determine whether or not a probability distribution is given. If a probability distribution is given, find its mean and standard deviation. If a probability distribution is not given, identify the requirements that are not satisfied.
Eye color-Groups of five babies are randomly selected. In each group, the random variable X is the number of babies with green eyes. The symbol 0+ denotes a positive probability value that is very small.
22) Let the random variable X represent the number of girls in a family of four children. Construct a table describing the probability distribution, then find the mean and standard deviation. (Hint- list the different possible outcomes.) Is it unusual for a family of three children to consist of 3 girls?
30) There is a 0.9968 probability that a randomly selected 50 year old female lives through the year. A Fidelity life insurance company charges $226 for insuring that the female will live through the year. If she does not survive the year, the policy pays out $50,000 as a death benefit.
a) From the perspective of the 50 year old female, what are the values corresponding to the two events of surviving the year and not surviving?
b) If the 50 year old female purchases the policy, what is her expected value?
c) Can the insurance company expect to make a profit from many such policies? Why?
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