Statistics and Probability Answers

. A housewife is asked to rank five brands of washing powder (A, B, C, D, E) in order of preference. Suppose that she actually has no preference and her ordering is arbitrary. What is the probability that: (a) brand A is ranked first; (b) brand C is ranked first and brand D is ranked second.

 100 people bought tickets in a charity raffle. 60 of them bought the tickets because they supported the charity. 75 bought tickets because they liked the prize. No one who neither supported the charity nor liked the prize bought a ticket. (a) What is the probability that the prize-winning ticket was bought by someone who liked the prize?

2.1. Let P(A) = 0.5, P(B) = 0.6 and P(A ∩ B) = 0.3. Find P(B¯), P(A ∩ B¯) and P(A ∪ B)

i. Suppose in a district grade 1 through grade 5, 60 percent of the population favor a particular school. A simple random sample of 350 is surveyed.

a. b. c. d. e.

What is the probability that at least 140 favor the school? What is the probability that at most 170 favor the school? What is the probability that more than 160 favor the school? What is the probability that fewer than 145 favor the school? What is the probability that exactly 180 favor the school?

ii. The annual

of downtown Memphis follows a Poisson distribution with mean 6.5.

number of earthquakes registering at least 2.5 on the Richter Scale and having an epicenter within 40 miles

a. What is the probability that at least 9 such earthquakes will strike next year?

b. What is the probability that at least 25 such earthquakes will strike during the next 5 years?

i. Family incomes have a mean of $60,000 with a standard deviation of $20,000. The data are normally distributed. What is the probability of a randomly chosen family having an income greater than $50 000?

ii. On average, weight of carry-on baggage of passengers on planes is 32.2 pounds. Assuming a standard deviation of 4.3 pounds, find the probability that the average weight of carry-on baggage of a random sample of 40 passengers exceeds 30 pounds.

iii. Suppose you are working with a data set that is normally distributed, with a mean of 150 and a standard deviation of 46. Determine the value of x from the following information. (Round your answers and z values to 2 decimal places.)

a. 60% of the values are greater than x. b. x is less than 16% of the values.

c. 25% of the values are less than x.

d. x is greater than 65% of the values.

The switchboard in a Police law office gets an average of 5.7 incoming phone calls during the noon hour on Mondays. Experience shows that the existing staff can handle up to six calls in an hour. Let X = the number of calls received at noon.

a. Find the mean and standard deviation of X.

b. What is the probability that the office receives at most six calls at noon on Monday?

c. Find the probability that the law office receives six calls at noon. What does this mean to the law office staff who get, on average, 5.5 incoming phone calls at noon?

d. What is the probability that the office receives more than eight calls at noon?

It has been determined that 5% of drivers checked at a road stop show traces of alcohol and 10% of drivers checked do not wear seat belts. In addition, it has been observed that the two infractions are independent from one another. If an officer stops five drivers at random:

a. Calculate the probability that exactly three of the drivers have committed any one of the two offenses.

b. Calculate the probability that at least one of the drivers checked has committed at least one of the two

offenses.

An agent sells life insurance policies to five equally aged, healthy people. According to recent data, the probability of a person living in these conditions for 30 years or more is 2/3. Calculate the probability that after 30 years:

a. All five people are still living.

b. At least three people are still living.

c. Exactly two people are still living.

Recall the example of rolling a six-sided die. This is an example of a discrete uniform random variable, so named because the probability of observing each distinct outcome is the same, or uniform, for all outcomes. Let Y be the discrete uniform random variable that equals the face-value after a roll of an eight-sided die. (The die has eight faces, each with number 1 through 8.) Calculate E(Y ), Var(Y ), and StdDev(Y )

Jaxson is a great free throw shooter. Over the last year he has made 88

%

88%

 of his free throws. If his probability stays consistent, what is the probability he will make his next three free throws? Show complete work on your worksheet!