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.

Assume that females have pulse rates that are normally distributed with a mean of mu equals 73.0 beats per minute and a standard deviation of sigma equals 12.5 beats per minute. Complete parts​ (a) through​ (c) below. a. If 1 adult female is randomly​ selected, find the probability that her pulse rate is less than 79 beats per minute. The probability is 0.6844 0.6844. ​(Round to four decimal places as​ needed.) b. If 16 adult females are randomly​ selected, find the probability that they have pulse rates with a mean less than 79 beats per minute. The probability is ----

The doorway of a specific style house is 71 inches. Men’s heights are normally distributed with a μ of 68.4 inches and σ of 1.9 inches. Women’s heights are normally distributed with a μ of 64.8 inches and a σ of 2.6 inches.

A. Determine the probability that a man can go through the doorway without bending.

B. Determine the probability that a woman can go through the doorway without bending.

C. Determine the probability that a sample of 9 men will have a μ> 71 inches.

D. Determine the probability that a sample of 16 women will have a μ > 71 inches.

E. Explain what all this means

Axline Computers manufactures personal computers at two plants, one in Texas and the other in Hawaii. The Texas plant has 35 employees; the Hawaii plant has 25. A random sample of 10 employees is to be asked to fill out a benefits questionnaire. (Round your answers to four decimal places.)

(a)

What is the probability that none of the employees in the sample work at the plant in Hawaii?

(b)

What is the probability that 1 of the employees in the sample works at the plant in Hawaii?

(c)

What is the probability that 2 or more of the employees in the sample work at the plant in Hawaii?

(d)

What is the probability that 9 of the employees in the sample work at the plant in Texas?

During the 2015–16 NBA season, Stephen Curry of the Golden State Warriors had a free throw shooting percentage of 0.908. Assume that the probability Stephen Curry makes any given free throw is fixed at 0.908, and that free throws are independent.

(a) If Stephen Curry shoots two free throws, what is the probability that he makes both of them?
(b) If Stephen Curry shoots two free throws, what is the probability that he misses both of them?
(c) If Stephen Curry shoots two free throws, what is the probability that he makes exactly one of them?

The fill amount of bottles of a soft drink is normally​ distributed, with a mean of 2.0 liters and a standard deviation of 0.07 liter. Suppose you select a random sample of 25 bottles.

a. What is the probability that the sample mean will be below 1.98 liters​?

b. What is the probability that the sample mean will be greater than 2.01 ​liters?

c. The probability is 99​% that the sample mean amount of soft drink will be at least how​ much?

d. The probability is 99​% that the sample mean amount of soft drink will be between which two values​ (symmetrically distributed around the​ mean)?

Round to three decimal places as​ needed

The masses of bottles produced by the Guinness factory in Ireland have a mean of 200 grams. Suppose the variance of the bottles is 175 grams. Round all answers to 3 decimals.

a. What is the probability that the mass of a randomly selected bottle is between 185 and 215 grams? If you can compute the exact probability, do so. If you cannot, then use an appropriate approximation.

b. Suppose that we have a sample of 34 bottles. What is the probability that the sample average mass is between 198.87 and 201.13 grams? If you can compute the exact probability, do so. If you cannot, then use an appropriate approximation.

Scores on Professor Combs' Statistics Final Exams have a long term history of being normally distributed, with a mean of μμ = 72 and a standard deviation of σσ = 9

a.) Find the probability that a single student will score above a 77 on the Final exam.

b.) Find the probability that a single student will score between a 67 and 77 on the Final exam.

c.) Find the probability that an entire class of 20 students will have a class average above a 77 on the exam.

d) Find the probability that an entire class of 20 students will have a class average between 67 and 77 on the Final exam.

A Bloomington resident commutes to work in Indiannapolis, and he encounters several traffic lights on the way to work each day. Over a period of time, the following pattern has emerged:

- Each day the first light is green

- If a light is green, then the next one is always red

- If he encounters a green light and then a red one, then the next will be green with probability 0.6 and red with probability .4.

- If he encounters two red lights in a row, then the next will be green with probability p and red with probability 1-p.

Formulate a Markov Chain model for this situation (Identify states and find the transition matrix).

Students enter the bathroom according to a Poisson process at a rate of 7.5 arrivals per minute.

1. What is the probability that exactly 46 students enter between 3:00 and 3:05?

2. Given that 6 students enter the bathroom between 4:00 and 4:01, what is the probability that exactly 36 students enter between 4:00 and 4:07?

3. Each student entering the bathroom has a .15 probability of wearing a hoodie, independent of other students. What is the probability that exactly 10 students wearing a hoodie enter the bathroom between 4: and 4:07?