An instructor who taught two sections of engineering statistics last term, the first with 25 students and the second with 35, decided to assign a term project. After all projects had been turned in, the instructor randomly ordered them before grading. Consider the first 15 graded projects.

(a) What is the probability that exactly 10 of these are from the second section? (Round your answer to four decimal places.)


(b) What is the probability that at least 10 of these are from the second section? (Round your answer to four decimal places.)


(c) What is the probability that at least 10 of these are from the same section? (Round your answer to four decimal places.)


(d) What are the mean value and standard deviation of the number among these 15 that are from the second section? (Round your mean to the nearest whole number and your standard deviation to three decimal places.)

(e) What are the mean value and standard deviation of the number of projects not among these first 15 that are from the second section? (Round your mean to the nearest whole number and your standard deviation to three decimal places.)

The Downtown Parking Authority of Tampa, Florida, reported the following information for a sample of 229 customers on the number of hours cars are parked and the amount they are charged. Number of Hours Frequency Amount Charged 1 18 $ 3 2 38 7 3 52 13 4 40 17 5 33 22 6 13 24 7 6 27 8 29 30 229 a. Convert the information on the number of hours parked to a probability distribution. (Round your answers to 3 decimal places.) Hours Probability 1 2 3 4 5 6 7 8 a-2. Is this a discrete or a continuous probability distribution? Discrete Continuous b-1. Find the mean and the standard deviation of the number of hours parked. (Do not round intermediate calculations. Round your final answers to 3 decimal places.) Mean Standard deviation b-2. How long is a typical customer parked? (Do not round intermediate calculations. Round your final answers to 3 decimal places.) The typical customer is parked for hours c. Find the mean and the standard deviation of the amount charged. (Do not round intermediate calculations. Round your final answers to 3 decimal places.) Mean Standard deviation

Suppose Alice flips 4 coins and Bob flips 4 coins. Find the probability that Alice and Bob get the exact same number of heads.

If a die is rolled 300 times, use the Chebyshev inequality to estimate the probability
that the number of occurrences of "three" does not lie strictly between 45 and 55.

restaurant is planning to add a bar – the bar can have only six barstools. Customers interested in having a drink at this bar arrive at a rate of 6 per hour following a Poisson distribution. It is expected that a customer stays 30 minutes, exponentially distributed. There are only 3 spaces available for customers to wait for a barstool to become available. Customers who want to come in and find there is no room to wait, go to the restaurant next door. Determine:
A. Probability that there are no customers at the bar.
B. The probability that an arriving customer has to wait for a barstool.
C. The average number of customers at the bar.
D. The average number of customers waiting.

4. * Suppose that jobs are sent to a printer at an average rate of 10 per hour. (a) Let X = the number of jobs sent in an hour. What is the distribution of X? Give the name and parameter values. (b) What is the probability that exactly 8 jobs are sent to the printer in an hour? (c) Let X = the number of jobs sent in a 12 min period. What is the distribution of X? Give the name and parameter values. (d) What is the probability that at least 3 jobs will be sent to the printer in a 12 min period? (e) How many jobs do you expect to be sent to the printer in a 12 min period?

Scores for a common standardized college aptitude test are normally distributed with a mean of 496 and a standard deviation of 101. Randomly selected men are given a Test Prepartion Course before taking this test. Assume, for sake of argument, that the test has no effect.

If 1 of the men is randomly selected, find the probability that his score is at least 547.1.
P(X > 547.1) =
(Enter your answer as a number accurate to 4 decimal places)

If 10 of the men are randomly selected, find the probability that their mean score is at least 547.1.
P(¯¯¯XX¯   > 547.1) =
(Enter your answer as a number accurate to 4 decimal places)

Off the coast of a highly populated island, there have been a number of fatal sharks over the years. It was found the the average number of fatal shark attacks per year is 11.1.

Round all probabilities to four decimal places.

(a) Find the probability there are exactly 9 fatal shark attacks off the coast of this island in any given year.

(b) Find the probability that there at least 9 fatal shark attacks off the coast of this island in any given year.

(c) It would be unusual to have more than fatal shark attacks off the coast of this island in any given year.

1) Suppose you start at a point and every minute you flip a coin. If the coin is head you move 1 foot north. If it is tails you stay in the same spot. A) At n minutes, what is the exact probability distribution of the number of feet north you have moved. B) What is the standard deviation of the number of feet you have moved. C) After 2000 minutes what is the approximate probability you have moved between 955 and 1045 feet north? (Hint, using the mean and the standard deviation, and assume that the random variable is approximately normal)

A girl scout and her mom are setting up a table to sell cookies in front of a grocery store. They have available 3 boxes of Samoas, 4 boxes of Tagalons, 6 boxes of Do-si-dos, and 7 boxes of Trefoils. Each box sells for $5.

a.) Define random variable you will need.

b.) Determine the probability distribution and parameters for the random variable defined.

c.) Suppose that, after two hours, ten boxes of cookies have been purchased. Determine the cumulative distribution function for the number of Samoas purchased.

d.) Draw the probability distribution function for the number of Samoas purchased.