Ch. 5 Practice Test due 2/27

An ecologist studying starfish populations records values for each of the following variables from randomly selected plots on a rocky coastline.

Read over the following variables:

How many of these are continuous random variables and how many are discrete?

Which of the following is closest to the 28th percentile in the standard normal distribution?

A hat holds a large number of slips of paper, each with a single digit from 0 to 4 on it. Which one of the following is a possible probability distribution for X = the number on a randomly selected slip of paper?

Check 5.1 for the properties of a valid probability model.

A private school has 25 students in each of grades 1 through 12. The principal randomly selects 1 student from each grade and records whether or not the student is over 5 feet tall. Let X = the number of students in the sample who are over 5 feet tall.

Which of the following requirements for a binomial setting is violated in this case?

Hint: check the meanings of B I N S.

The figure shows the density curve that is the probability distribution of a continuous random variable. Seven values are marked on the density curve.

Which two of the following statements are true?

Questions 6 and 7 refer to the following setting.

A psychologist studied the number of puzzles that subjects were able to solve in a 5-minute period while listening to soothing music. Let X be the number of puzzles completed successfully by a randomly chosen subject.

The psychologist found that X had the following probability distribution:

What is the expected number of puzzles a subject could solve in the 5-minute period while listening to soothing music?

Check Lesson 5.2 for an example.

Questions 6 and 7 refer to the following setting.

A psychologist studied the number of puzzles that subjects were able to solve in a 5-minute period while listening to soothing music. Let X be the number of puzzles completed successfully by a randomly chosen subject.

The psychologist found that X had the following probability distribution:

What is the probability that a randomly chosen subject completes more than the expected number of puzzles in the 5-minute period while listening to soothing music?

Remember to use your answer to the previous question.

The standard deviation of X is 0.9. Which of the following is the best interpretation of this value?

Lesson 5.5 part 1

For the normal distribution shown:

The standard deviation is closest to which of the values below.

Hint: refer to your half sheet for help.

In the game Pass the Pigs, a small plastic pig is rolled, and its orientation when it comes to a stop determines the number of points a player scores. Approximately 9% of rolls produce a “trotter”—that is, the pig lands right side up, standing on its four feet.

Suppose you roll a pig 10 times.

Which of the following expressions represents the probability that you roll exactly 2 trotters?

If the heights of a population of men follow a normal distribution, and 99.7% have heights between 5 feet 0 inches and 7 feet 0 inches, what is your estimate of the standard deviation of the heights in this population?

Hint: remember there are 12 inches in one foot

Check your half sheet for the visual for the 68-95-99.7 Rule

Let Y denote the number of broken eggs in a randomly selected carton of one dozen “store brand” eggs at a local supermarket. Suppose that the probability distribution of Y is as follows.

What is the probability that at least 2 eggs in a randomly selected carton are broken?

Let Y denote the number of broken eggs in a randomly selected carton of one dozen “store brand” eggs at a local supermarket. Suppose that the probability distribution of Y is as follows.

Calculate and interpret the mean of Y.

Lesson 5.1 & 5.2, remember mean is the same thing as Expected Value.

Let Y denote the number of broken eggs in a randomly selected carton of one dozen “store brand” eggs at a local supermarket. Suppose that the probability distribution of Y is as follows.

I used statsmedic to find the standard deviation, it is 0.837. Interpret the standard deviation of Y using context.

An airline claims that its 7:00 A.M. New York to Los Angeles flight has an 85% chance of arriving on time on a randomly selected day. Assume for now that this claim is true. Suppose we take a random sample of 20 of these flights. Let X = the number of flights that arrive on time.

Explain why X is a binomial random variable using B I N S.

An airline claims that its 7:00 A.M. New York to Los Angeles flight has an 85% chance of arriving on time on a randomly selected day. Assume for now that this claim is true. Suppose we take a random sample of 20 of these flights. Let X = the number of flights that arrive on time.

Use the binomial probability formula to find P(X = 19).

Round to three placees.

Use your answer from above when you found P(X=19). Interpret this value in context, what does it mean?

An airline claims that its 7:00 A.M. New York to Los Angeles flight has an 85% chance of arriving on time on a randomly selected day. Assume for now that this claim is true. Suppose we take a random sample of 20 of these flights. Let X = the number of flights that arrive on time.

Calculate the mean of X.

An airline claims that its 7:00 A.M. New York to Los Angeles flight has an 85% chance of arriving on time on a randomly selected day. Assume for now that this claim is true. Suppose we take a random sample of 20 of these flights. Let X = the number of flights that arrive on time.

Calculate the standard deviation of X. Round to three places past the decimal.

An airline claims that its 7:00 A.M. New York to Los Angeles flight has an 85% chance of arriving on time on a randomly selected day. Assume for now that this claim is true. Suppose we take a random sample of 20 of these flights. Let X = the number of flights that arrive on time.

What is the probability that only 14 of the 20 flights arrive on time? Calculate P(X = 14)

Round your answer to three places past the decimal.

An airline claims that its 7:00 A.M. New York to Los Angeles flight has an 85% chance of arriving on time on a randomly selected day. Assume for now that this claim is true. Suppose we take a random sample of 20 of these flights. Let X = the number of flights that arrive on time.

What is the probability that all of the 20 flights arrive on time? Calculate P(X = 20)

An airline claims that its 7:00 A.M. New York to Los Angeles flight has an 85% chance of arriving on time on a randomly selected day. Assume for now that this claim is true. Suppose we take a random sample of 20 of these flights. Let X = the number of flights that arrive on time.

What is the probability that at least one of the 20 flights arrives late?

Remember back to Chapter 4, what do we do if we want 'at least one'.

The Virginia Cooperative Extension reports that the mean weight of yearling Angus steers is 1152 pounds. Suppose the standard deviation is 84 pounds and a Normal Model is useful for making predictions. Using N(1152, 84) what percent of the steers weigh less than 1250 pounds?

The Virginia Cooperative Extension reports that the mean weight of yearling Angus steers is 1152 pounds. Suppose the standard deviation is 84 pounds and a Normal Model is useful for making predictions.

What percent of the steers weigh between 1062 and 1349 pounds?

Hint: Use your answer from #24 above for the percent less than 1062 pounds, then you only need to do calculations for 1349 pounds.