Suppose that a category of world class runners are known to run a marathon (26 miles) in an average of 145 minutes with a standard deviation of 15 minutes. Consider 49 of the races.

Let

X = the average of the 49 races.

• Part (a)

  Give the distribution of

  X.

  (Round your standard deviation to two decimal places.)

  X~  

• Part (b)

  Find the probability that the runner will average between 143 and 148 minutes in these 49 marathons. (Round your answer to four decimal places.)
  

• Part (c)

  Find the 80th percentile for the average of these 49 marathons. (Round your answer to two decimal places.)
    min

• Part (d)

  Find the median of the average running times.
    min

World class marathon runners are known to run that distance (26.2 miles) in an average of 146 minutes with a standard deviation of 15 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 140 minutes.

b.) The probability that 10 runners chosen at random have an average finish time of less than 140 minutes.  

c.) The probability that 50 runners chosen at random have an average finish time of less than 140 minutes.  

World class marathon runners are known to run that distance (26.2 miles) in an average of 146 minutes with a standard deviation of 15 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 140 minutes.

b.) The probability that 10 runners chosen at random have an average finish time of less than 140 minutes.  

c.) The probability that 50 runners chosen at random have an average finish time of less than 140 minutes.  

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 45 months and a standard deviation of 10 months. Using the 68-95-99.7 rule, what is the approximate percentage of cars that remain in service between 55 and 75 months?

World class marathon runners are known to run that distance (26.2 miles) in an average of 146 minutes with a standard deviation of 14 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 140 minutes.

b.) The probability that 10 runners chosen at random have an average finish time of less than 140 minutes.

c.) The probability that 50 runners chosen at random have an average finish time of less than 140 minutes.

At noon, ship A is 10 nautical miles due west of ship B. Ship A is sailing west at 16 knots and ship B is sailing north at 21 knots. How fast (in knots) is the distance between the ships changing at 4 PM? (Note: 1 knot is a speed of 1 nautical mile per hour.)?

The area of a healing wound is given by A=πr2A=πr2. The radius is decreasing at the rate of 4 millimeters per day at the moment when r=30r=30. How fast is the area decreasing at that moment?

Gravel is being dumped from a conveyor belt at a rate of 40 cubic feet per minute. It forms a pile in the shape of a right circular cone whose base diameter and height are always equal. How fast is the height of the pile increasing when the pile is 11 feet high?
Recall that the volume of a right circular cone with height h and radius of the base r is given by
V=13πr2hV=13πr2h

A spherical snowball is melting in such a way that its radius is decreasing at rate of 0.1 cm/min. At what rate is the volume of the snowball decreasing when the radius is 16 cm. (Note the answer is a positive number).

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 there is no difference in the durability of the four kinds of tires at the 0.05 level of significance. Using the above data, test the null hypothesis that the failure rates of the four tire brands are 10% at the 0.05 level of significance.

1. The longevity of truck tires (in thousands of miles) follows a normal distribution with mean µ and standard deviation σ = 20. Suppose n = 64 tires are randomly selected and the sample mean ¯ x = 76.5.

(a) Test H0 : µ = 75 versus Ha : µ 6= 75 at the α = 0.05 significance level using a 3-step test.

(b) Based upon your answer in part (a), does µ significantly differ from 75? Why?

(c) Find the p−value for the test in part (a).

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 42 months and a standard deviation of 6 months. Using the 68-95-99.7 rule, what is the approximate percentage of cars that remain in service between 54 and 60 months?

Consider a car traveling on a highway. If the car travels 100 miles in 2 hours, which theorem guarantees that the car must have been traveling at 50 mph at some point in those two hours? (You may assume position and velocity are continuous and differentiable)