World class marathon runners are known to run that distance (26.2 miles) in an average of 143 minutes with a standard deviation of 13 minutes.

If we sampled a group of world class runners from a particular race, find the probability of the following:

**(use 4 decimal places)**

a.) The probability that one runner chosen at random finishes the race in less than 137 minutes.

b.) The probability that 10 runners chosen at random have an average finish time of less than 137 minutes.

c.) The probability that 50 runners chosen at random have an average finish time of less than 137 minutes.

The following data represent the speed of a car (in miles per hour) and its breaking distance (in feet) on dry asphalt.

b) Find the least squares regresssion line. Round the slope and y-intercept to two decimals.

B(x) =   

(c) Find the linear correlation coefficient. Round your answer to 4 decimals.

r =   

(d) Comment on whether a linear model is a good model. Explain why. This part will be hand graded.



(e) Predict the breaking distance if you were going 65 miles per hour. Use your rounded values from part (b).



(f) What speed would you be traveling at if you needed 200 feet to break? Use your rounded values from part (b).

A large university claims that the average cost of housing within 5 miles of the campus is $ 8900 per school year. A high school student is preparing her budget for her freshman year at the university. She is concerned that the university‘s estimate is too low. She obtains a random sample of 81 records and computes the average cost is $ 9050. Based on earlier data, the population standard deviation is $ 760. Use α=0.01 level of significance.

a) Step 1: State the null and alternative hypotheses.

b) Step 2: Write down the appropriate test statistic and the rejection region of your test (report zcritical(s))

c) Step 3: Compute the value of the test statistic (z observed)

d) Step 4: State your conclusion (in one sentence, state whether or not the test rejects the null hypothesis and in another sentence apply the results to the problem).

e) Compute the p- value for this test. Is the evidence strong or weak in supporting the alternative hypothesis?

A major hurricane is a hurricane with wind speeds of 111 miles per hour or greater. During the last​ century, the mean number of major hurricanes to strike a certain​ country's mainland per year was about 0.59 Find the probability that in a given year​ (a) exactly one major hurricane will strike the​ mainland, (b) at most one major hurricane will strike the​ mainland, and​ (c) more than one major hurricane will strike the mainland.

A company has a policy of retiring company cars; this policy looks at number of miles driven, purpose of trips, style of car and other features. The distribution of the number of months in service for the fleet of cars is bell-shaped and has a mean of 57 months and a standard deviation of 11 months. Using the empirical (68-95-99.7) rule, what is the approximate percentage of cars that remain in service between 24 and 46 months? Ans = % (Do not enter the percent symbol. This asks for a percentage so do not convert to decimal. For example, for 99%, you would enter 99, not 0.99)

A company has a policy of retiring company cars; this policy looks at number of miles driven, purpose of trips, style of car and other features. The distribution of the number of months in service for the fleet of cars is bell-shaped and has a mean of 55 months and a standard deviation of 8 months. Using the 68-95-99.7 rule, what is the approximate percentage of cars that remain in service between 31 and 47 months?

A company has a policy of retiring company cars; this policy looks at number of miles driven, purpose of trips, style of car and other features. The distribution of the number of months in service for the fleet of cars is bell-shaped and has a mean of 64 months and a standard deviation of 9 months. Using the empirical rule (as presented in the book), what is the approximate percentage of cars that remain in service between 82 and 91 months?

ans =  %

Suppose that a category of world class runners are known to run a marathon (26 miles) in an average of 146 minutes with a standard deviation of 12minutes. Consider 49 of the races.

Let X = the average of the 49 races.

a)Give the distribution of X. (Round your standard deviation to two decimal places.)

X~___(___,___)

b)Find the probability that the average of the sample will be between 145 and 148 minutes in these 49 marathons. (Round your answer to four decimal places.)

_________

c) Find the 70th percentile for the average of these 49 marathons. (Round your answer to two decimal places.)

_____min

d) Find the median of the average running times.

____min

Suppose that 26 of 200 tires of brand A failed to last 30,000 miles whereas the corresponding figures for 200 tires of brands B, C, and D were 23, 15, and 32. Test the null hypothesis that the failure rates of the four tire brands are 10% at the 0.05 level of significance.