1. the Average Age of Amtrak Cars Is 20 Years. If the Distribution of Age Is Normally

1. the average age of amtrak cars is 20 years. If the distribution of age is normally distributed and 22% of the cars are older than 23 years, find the standard deviation (σ).

For 22% top area, z = 0.772

Z= (x-mu)/sigma

Or, 0.772= (23-20)/sigma

Or, sigma = 3/0.772 = 3.886
2. Given n = 36, x̅ = 211, σ = 23, compute a 96% confidence interval (C.I.) for μ.

Std dev. = 23/sqrt(36) = 3.833

96% CI: [203.126 218.874]
3. Use the binomial probability formula (not the binomial probability distribution table in the appendix) to find the probability of getting 2 or 3 correct responses among 6 different requests from AT&T assistance. AT&T assures us that they are correct 91% of the time.

P(2 or 3) = 6C2*0.91^2*0.09^4+6C3*0.91^3*0.09^3

=0.0118
4. Rita is playing Monopoly with her very best friend Cher. On her next move, Rita must throw a sum bigger than 8 on her two dice in order to land on her own property and pass "Go". What is the probability that she will roll a sum larger than 8?

P = 10/36 as 10 possibilities for more than 8 in total 36 possibilities.

= 5/18
5. The owner of Jim's Gas Station wishes to determine the proportion of customers who use a credit card to pay at the pump. He surveys 100 customers and finds that 75 paid at pump. Develop a 90% C.I. for the population proportion.

P = 75/100 = 0.75

Sigma = sqrt(0.75*0.25/100)=0.0433

90% CI: 0.679 0.821
6. Find the correlation coefficient with the data for X and Y.
X- 3, 4, 5, 6
Y- 6, 9, 11, 11
7. Find the equation for the regression line based on the same data given in the previous problem (#6). Give a rough illustration of the corresponding graph.