statistics/probability

According to the highway department in Praire City, Idaho, the number of passengers per care (including driver) commuting on highway 57 per evening is defined by the probability distribution

Number of Passengers  X Probability P(x)

1  0.35 

2  0.35 

3  0.15

4  0.10 

5  0.05

For this probability distribution

a) Identify the values of the random variable

b) Construct a probability histogram and determine its shape

c) Verify that the sum of all the probabilities is one

d) What is the expected number of passengers each evening?

e) Calculate the standard deviation

f) How unusual is it for a car to contain more than 2 passengers? Explain.

Recently, it was reported that a baby born in 2014 is expected to live to a mean age of 79 years. If the standard deviation for this population is 10 year, use the Central Limit Theorem to answer questions about sampling distribution of the mean formed by taking from the population of babies born is 2014, all possible random samples of size 100.

A) Find μx̄

B) Determine σx̅

C) Can this sampling distribution of the mean be approximated by a normal distribution

D) IF the population of life expectancies for those born in 2014 is approximately normal, what is the probability that a baby born in 2014 will live to: Atleast 78? At leave age 82?

E) If a random sample of 100 babies born in 2014 were selected, what is the probability that these babies will live to at least a mean age of 78? To at least a mean age of 82?

F) why are the answers to parts (d) and (e) different?