Statistic 5-7

Suppose that the longevity of a light bulb has a mean lifetime of eight years. If a bulb has already lasted 12 years, find the prob. that it will last a total of over 19 years.

e^ (-7/8) or .4167

A center receives about ten emails every half hour. What is the prob that the center receives more than four emails in the next six minutes?

0.0527

In a bag, there are six red marbles and four green marbles. The red marbles are marked with the numbers 1,2,3,4,5 and 6. The green marbles are marked 1,2,3, and 4. What is the sample space? What is P(G AND O)?

0.2

A school has 200 seniors of whom 140 will be going to college next year. Forty will be going directly to work. The remainder are taking a gap year. Fifty of the seniors going to college play sports. Thirty of the seniors going directly to work play sports. Five of the seniors taking a gap year play sports. What is the prob. that a senior is going to college and plays sports?

0.2499

Helen plays basketball. For free throws, she makes the shot 75% of the time. Helen must now attempt two free throws. C = the event that Helen makes the first shot. P ( C ) = 0.75. D = the event Helen makes the second shot. P ( D ) = 0.75. The probability that Helen makes the second free throw given that she made the first is 0.85. What is the probability that Helen makes both free throws?

0.6375

Draw two cards from a standard 52-card deck with replacement. Find the prob. of getting at least one black cards.

0.75

The number of days ahead travelers purchase their airline tickets has the average amount of time equal to 15 days. Find the prob that a traveler will purchase a ticket fewer than ten days in advance. How many days do half of all travelers wait?

10.3972

You are playing a game of chance in which four cards are drawn from a standard deck of 52 cards. You guess the suit of each card before it is drawn. The cards are replaced in the deck on each draw. You pay $1 to play. If you guess the right suit every time, you get your money back and $256. What is your expected profit of playing the game over the long term?

127/2 or $63.50

How many 6 digit telephone numbers can be formed if each number starts with 35 and no digit appears more than once?

1680

Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed?

25200

In how many different ways can the letters of the word 'CORPORATION' be arranged so that the vowels always come together?

50400

Suppose the time it takes a student to finish a quiz is uniformly distributed between six and 15 minutes inclusive. Find the prob that a random student needs at least eight minutes to compete the quiz. Then find the prob that a different student needs at least eight minutes to finish the quiz given that she has already taken more than seven minutes.

P (x > 8) = 0.7778 P (x > 8 | x > 7) = 0.875

Let event A = learning Spanish. Let event B = learning German. Then A AND B = learning Spanish and German. Suppose P(A) = 0.4 and P(B) = 0.2. P(A AND B) = 0.08. Are events A and B independent? Show ONE of the following P(AIB) = P(A) P(BIA) P(A AND B) = P(A)P(B)

P(A|B)=P (A AND B) / P(B) = 0.08 / 0.2 = 0.4 = P(A) The events are independent because P(A|B) = P(A).

About 32% of students participate in a community volunteer program outside of school. If 30 students are selected at random, find the probability that at most 14 of them participate in a community volunteer program outside of school.

a) 0.03588 b) 0.9695

A student goes to the library. Let events B = the student checks out a book and D = the student checks out a DVD. Suppose that P(B) = 0.40, P(D) = 0.30 and P(DIB) = 0.5. a) Find P(B') b) Find P(D AND B) c) Find P(BID) d) Find P(D AND B') e) Find P(DIB')

a) 0.60 b) 0.20 c) 0.66 d) 0.10 e) 0.06

In a recent study reported Oct.29, 2012 on the Flurry Blog, the mean age of tablet users is 35 years. Suppose the standard deviation is ten years. The sample size is 39. a) What are the mean and standard deviation for the sum of the ages of tablet users? What is the distribution? b) Find the probability that the sum of the ages is between 1,400 and 1,500 years. c) Find the 90th percentile for the sum of the 39 ages.

a) 106.01 b) 0.7974 c) 1789.3

A student goes to the library. Let events B = the student checks out a book and D = the student checks out a DVD. Suppose that P(B) = 0.40, P(D) = 0.30 and P(B AND D) = 0.20. a) Find P(BID) b) Find P(DIB) c) Are B and D independent? d) Are B and D mutually exclusive?

a) 2/3 b) 1/2 or 0.5 c) not independent d) No b/c there is an intersection-- some students can rent out a DVD and a book.

The literacy rate for a nation measures the proportion of people age 15 and over who can read and write. The literacy rate for women in Afghanistan is 12%. Let X = the number of Afghani women you ask until one says that she is literate. a) What is the prob distribution of X? b) What is the prob. that you ask five women before one says she is literate? c) What is the prob. that you must ask ten women? d) Find the mean and standard deviation of X.

a) X∼G(0.12) b) 0.0720 c) 0.0380 d) mean = 8. 333 standard deviation = 7.817

The total duration of baseball games is uniformly distributed between 447 hours and 521 hours inclusive. a) Find a and b and describe what they represent b) Write the distribution c) Find the mean and standard deviation. d) What is the prob. that the duration of games is between 480 and 500 hrs? e) What is the 65th percentile for the duration of games?

a) a is 447, and b is 521. a is the minimum duration of games for a team for the 2011 season, and b is the maximum duration of games for a team for the 2011 season. b) X ~ U(447, 521) c) μ = 484, and σ = 21.36 d) P(480 < x < 500) = 0.2703 e) 495.1 hours

On average, a pair of running shoes can last 18 months if used every day. a) What is the prob that a pair of shoes last more than 15 months? b) On average, how long would six pairs of running shoes last if they are used one after the other? c) Eighty percent of running shoes last at most how long if used every day?

a) e^-5/6 or 0.4346 b) 108 c) 28.9699

Suppose that the distance, in miles, that people are willing to commute to work has a decay parameter of 1/20. Let X= the distance people are willing to commute in miles. a) What is m, the mean, and standard deviation? b) What is the prob that a person is willing to commute more than 25 miles?

a) m = 1/20 mean = 20 standard deviation = 20 b) e^(-5/4) = 0.2865