1. Assume that daily TV viewing is normally distributed and has a mean of 8 hours per household with a standard deviation of 2 hours. Find the following probabilities:

1. Probability that a randomly selected household views TV more than 10 hours a day, i.e. P( x > 10)
2. Probability that a randomly selected household views TV more more than 11 hours a day, i.e. P(x > 11)
3. Probability that a randomly selected household views TV less than 3 hours a day, i.e. P(x < 3)
4. Probability that a randomly selected household views TV between 10 and 12 hours a day, i.e. P( 10 < x < 12)

A university conducted a survey of

381

undergraduate students regarding satisfaction with student government. Results of the survey are shown in the table by class rank. Complete parts​ (a) through​ (d) below.

   Freshman   Sophomore   Junior   Senior
Satisfied 54   48   64   60
Neutral 30   20   17   14
Not satisfied   25   19   10   20

​(a) If a survey participant is selected at​ random, what is the probability that he or she is satisfied with student​ government?

​(b) If a survey participant is selected at​ random, what is the probability that he or she is a​ junior?

​(c) If a survey participant is selected at​ random, what is the probability that he or she is satisfied and a​ junior?

​(d) If a survey participant is selected at​ random, what is the probability that he or she is satisfied or a​ junior?

(a) What is the probability that a randomly selected student in Dr. Alan  Math course is a Sophomore?

(b) What is the probability that a randomly selected student will make a D in Dr. Alan  Math course?

(c) Given that a particular student made a B or better in Dr. Alan  Math course, what is the probability that he or she took the course as a Junior?

(d) Given that a particular student in Dr. Alan Math  course is a Senior, what is the probability that he or she will make an A in the course?

Brady is a figure skater. He finds a few of the jumps he does to be difficult, but the rest are easy for him. He must include four jumps in his routine. He always makes the first jump a difficult one. After a difficult jump, there is a 0.4 probability that he'll do another difficult jump, and otherwise he'll do an easy one. After an easy jump, there is a 0.2 probability that he'll do another easy one, and otherwise he'll do a hard one.  

What is the probability that the final (fourth) jump of his routine will be an easy one?    

What is the probability that all four jumps of his routine will be difficult ones?    
Enter your answers as whole numbers or decimals.

Customers arrive at a department store according to a Poisson process with an average of 12 per hour.

a. What is the probability that 3 customers arrive between 12:00pm and 12:15pm?

b. What is the probability that 3 customers arrive between 12:00pm and 12:15pm and 6 customers arrive between 12:30pm and 1:00pm?

c. What is the probability that 3 customers arrive between 12:00pm and 12:15pm or 6 customers arrive between 12:30pm and 1:00pm?

d. What is the probability that a total of 10 customers arrive between 12:00pm and 12:15pm and 12:45pm and 1:00pm? That is, the total count is 10 for both of these time intervals combined.

The probability that a randomly selected 2 ​-year-old male chipmunk will live to be 3 years old is 0.98632 . ​(a) What is the probability that two randomly selected 2 ​-year-old male chipmunk s will live to be 3 years​ old? ​(b) What is the probability that nine randomly selected 2 ​-year-old male chipmunk s will live to be 3 years​ old? ​(c) What is the probability that at least one of nine randomly selected 2 ​-year-old male chipmunk s will not live to be 3 years​ old? Would it be unusual if at least one of nine randomly selected 2 ​-year-old male chipmunk s did not live to be 3 years​ old?

Problem 2.2 Consider a production system consisting of three Bernoulli
machines and a controller, which also obeys the Bernoulli reliability model. This
production system is considered up if the controller and at least two machines are
up. During each cycle, the controller is up with probability 0.8 and each machine
is up with probability 0.9. The controller and the machines fail independently.
(a) Calculate the probability that the production system is up.
(b) Assume that a second controller, identical to the first one, is added to the
system, and the re-designed system is up if at least one controller and two
machines are up. Calculate the probability that the re-designed production
system is up.
(c) Explain the reason for the difference between the two numbers you calculated.

Assume that females have pulse rates that are normally distributed with a mean of

mu equals 74.0μ=74.0

beats per minute and a standard deviation of

sigma equals 12.5σ=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 between

70 beats per minute and 78

beats per minute.

A) The probability is .2510

​(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 between

70 beats per minute and 78 beats per minute.The probability is________

​(Round to four decimal places as​ needed.)

In an urn, there are 5 red balls, 5 green balls, 4 yellow balls, and 6 white balls. You are drawing balls without replacement.

a. When you draw the first ball, what is the probability that the ball will be white?

b. Let us assume that you have drawn two balls and both of them are green. What is the probability that the next ball drawn will be green?

c. Let us assume that the third ball drawn is also green like the first two balls. What is the probability that the fourth ball drawn is white?

d. Let us assume that a fourth ball is drawn, but the color is not revealed to you. What is the probability that the fifth ball drawn is white?

There are two types of potential borrowers in equal numbers among the population. All have projects that require an investment of $100, which must be borrowed. Type A projects yield a gross return of $130 in one year with probability .8; they fail and yield 0 with probability .2. Type B projects yield a gross rate of return of $250 with probability .4, but fail, yielding zero, with probability .6. Potential lenders require a gross return of $102 on $100 loaned. With symmetric information, who will get financing and why? Now suppose the project expected returns are private information. Lenders cannot distinguish one type from another. Will any lending occur? Why or why not? Explain in detail.