According to the U.S. National Center for Health Statistics, there is a 98% probability that a 20-year-old male will survive to age 30.

(a) Using statistical software, simulate taking 100 random samples of size 30 from this population.

(b) Using the results of the simulation, compute the probability that exactly 29 of the 30 males survive to age 30.

(c) Compute the probability that exactly 29 of the 30 males survive to age 30, using the binomial probability distribution. Compare the results with part (b).

(d) Using the results of the simulation, compute the probability that at most 27 of the 30 males survive to age 30.

(e) Compute the probability that at most 27 of the 30 males survive to age 30 using the binomial probability distribution. Compare the results with part (d).

(f) Compute the mean number of male survivors in the 100 simulations of the probability experiment. Is it close to the expected value?

(g) Compute the standard deviation of the number of male survivors in the 100 simulations of the probability experiment. Compare the result to the theoretical standard deviation of the probability distribution.

(h) Did the simulation yield any unusual results?