Exam 11: Probability Basics

Use the following In 2008, the Detroit Lions set an NFL record by losing all 16 regular season games. Suppose that the Lions actually had a 10% chance of winning an individual game in the 2008 season and that each game was independent. Let X represent the number of wins out of 16 regular season games. Round all answers to three decimal places unless otherwise specified. -What is the probability of winning 1 or 2 games?

Use the following On the first day of class, students in a large introductory statistics course were asked their sex and eye color. The results are summarized in the provided table. Round your answer to each question to three decimal places. -Are male and blue eyes independent? Briefly justify your answer.

Use the following A statistician used a computer to generate 4 random values between 0 and 9. Let X represent the number of these values that are 5 or larger. Round all probability calculations to three decimal places. -Find the standard deviation of the random variable X.

Use the following About 80% of people have seen television ads for a certain product. Of the individuals who see the ad, only 1% buy the product. Of the individuals who do not see the ad, 0.5% buy the product. Round all answers to three decimal places. -What is the probability that a randomly selected individual has bought the product?

Use the following Calculate the requested quantity. -

Use the following When a certain pitcher throws his fastball, 75% of the time it is a strike. Suppose he throws 20 fastballs and that the pitches are independent of one another. Let X represent the number of strikes in 20 pitches. Round all answers to three decimal places. -What is the probability that all 20 pitches are strikes?

Use the following In the classic dice game Yahtzee, players roll five dice and score points by obtaining different combinations of values. Consider rolling five fair dice. Let X represent the number of sixes in a single roll of the five dice. Unless otherwise specified, round all answers to three decimal places. -Find the standard deviation of the number of sixes is a roll of five fair dice.

Use the following A random variable X has the following probability function: Round all answers to two decimal places. -Compute the standard deviation of the random variable X.

Use the following A random variable X has the following probability function: Round all answers to two decimal places. -Find P(X = 1 or X = 2).

Use the following Let A and B be two events such that P(A) = 0.35, P(B) = 0.45, and P(A and B) = 0.1575. Use two decimal places in your answer unless otherwise specified. -Find P(A if B).

Use the following Let A and B be two events such that P(A) = 0.35, P(B) = 0.45, and P(A and B) = 0.1575. Use two decimal places in your answer unless otherwise specified. -Find P(not B).

Use the following A statistician used a computer to generate 4 random values between 0 and 9. Let X represent the number of these values that are 5 or larger. Round all probability calculations to three decimal places. -What is the probability that all 4 values are 5 or larger?

Use the following About 25.4% of Iowa residents are classified as obese. Suppose we take a random sample of 200 Iowa residents. Let X represent the number of residents that are obese. Round all answers to three decimal places unless otherwise specified. -Find the standard deviation of the random variable X.

Use the following The New York Lottery has a daily game called "Take Five" where you win prizes based on how many of the 5 selected numbers match your ticket. The probability function for the number of correct picks on a ticket (X) is displayed in the provided table. Round all answers to three decimal places. -Compute the variance of the number of correct picks on a "Take Five" ticket.

Use the following In the game Pass the Pigs, players score (or lose) points by rolling a pair of rubber pigs. The number of points scored depends upon the configuration of the pigs when they land. A paper that appeared in the Journal of Statistics Education (Volume 14, Number 3, 2006) describes a dataset obtained by rolling the pigs many times. The probability function for the number of points scored on a roll (X) is displayed in the following table: Round all answers to two decimal places. -Compute the variance of the number of points scored on a roll.

Use the following A computer science student is writing a simplified version of the classic murder-mystery game Clue for his class project. In his implementation, there are three equally likely suspects: Miss Scarlet, Colonel Mustard, and Professor Plum. If Miss Scarlet is the murderer, there is a 40% chance she uses the knife, 35% chance she uses the lead pipe, and a 25% chance she uses the rope. If Colonel Mustard is the murderer, there is a 20% chance he uses the knife, a 30% chance he uses the lead pipe, and a 50% chance he uses the rope. If Professor Plum is the murderer, there is a 30% chance he uses the knife, a 40% chance he uses the lead pipe, and a 30% chance he uses the rope. Round all answers to three decimal places. -What is the probability that the lead pipe is the murder weapon?

Use the following Let A and B be two events such that P(A) = 0.35, P(B) = 0.45, and P(A and B) = 0.1575. Use two decimal places in your answer unless otherwise specified. -Find P(not A).

Use the following About 25.4% of Iowa residents are classified as obese. Suppose we take a random sample of 200 Iowa residents. Let X represent the number of residents that are obese. Round all answers to three decimal places unless otherwise specified. -What is the probability that exactly 56 people are obese?

Use the following Use the provided tree diagram to find the requested probabilities. Round all answers to three decimal places. -P(A if X)

Use the following There are three roofing companies that service a small community. Al's Roof Repair gets 45% of the roofing jobs in the community while Bob's Better Building and Carl's Roof Service get 25% and 30% of the business, respectively. Of Al's customers, 70% are satisfied. Of Bob's customers, 95% are satisfied. Among Carl's customers, 90% are satisfied. Round all answers to four decimal places. -What proportion of roofing customers are satisfied?