{{asɛmtiNe Ɔkyerɛwfo}} | Nhomakorabea | Nneɛma a ɛma wotumi yɛ ade

4

Classify each variable as a discrete or continuous random variable

The amount of sugar in an orange
The Friday night attendance at a football game
The number of children in a family
The age of a female

Discrete
Continuous
None

2

In a probability distribution, the Probability must satisfy which two requirements?

The sum of the probabilities must add up to 1.

The values of random variable X must be between 0 and 1.

The distribution must be symmetric.

Each individual probability must be greater than or equal to 0 but less than or equal to 1.

The values of random variable X must add up to 1.

The table below shows the probability distribution for th enumber of tails (X) in five tosses of a fair coin.

1

What is the expected value of X?

1

Suppose that the distribution of a set of scores has a mean of 47 and a standard deviation of 14. If 4 is added to each score, what will be the mean and the standard deviation of the distribution of new scores?

Mean is 51 and Standard Deviation is 18

Mean is 47 and Standard Deviation is 14

Mean is 47 and Standard Deviation is 16

Mean is 47 and Standard Deviation is 18

Mean is 51 and Standard Deviation is 14

1

Roll one 8-sided die 10 times. The probability of getting exactly 3 sevens in those 10 rolls is given by

1

Let the random variable X represent the profit made on a randomly selected day by a certain store. Assume that X is Normal with mean $360 and standard deviation $50. What is P(X > $400)?

1

A dealer in the Sands Casino in Las Vegas selects 40 cards from a standard deck of 52 cards. Let Y be the number of red cards (hearts or diamonds) in the 40 cards selected. Which of the following best describes this setting

Y has a geometric distribution with n = 52 observations and probability of success p = 0.5.

Y has a binomial distribution with n = 40 observations and probability of success p = 0.5, provided the deck is shuffled well.

Y has a binomial distribution with n = 40 observations and probability of success p = 0.5, provided that after selecting a card it is replaced in the deck and the deck is shuffled well before the next card is selected.

Y has a geometric distribution with n = 40 observations and probability of success p = 0.5.

Y has a binomial distribution with n = 40 observations and probability of success p = 0.5

1

In a large population of college students, 20% of the students have experienced feelings of math anxiety. If you take a random sample of 10 students from this population, the mean and standard deviation of the number of students in the sample who have experienced math anxiety is:

mean is 2 and standard deviation is 1.414

mean is 2 and standard deviation is 1.265

mean is 2 and standard deviation is 1.6

mean is 1.6 and standard deviation is 1.265

mean is 1.6 and standard deviation is 1.414

1

Which of the following is a true statement?

A geometric random variable takes on integer values from 0 to n

An important difference between binomial and geometric random variables is that there is a fixed number of trials in a binomial setting, and the number of trials varies in a geometric setting.

The binomial setting requires that there are only two possible outcomes for each trial, while the geometric setting permits more than two outcomes

The distribution of every binomial random variable is skewed right

If X is a geometric random variable and the probability of success is 0.85, then the probability distribution of X will be skewed left, since 0.85 is closer to 1 than to 0.

1

In order for the random variable X to have a geometric distribution, which of the following conditions must X satisfy?
I. p < 0.5
II. The number of trials is fixed.
III. Trials are independent.
IV. The probability of success has to be the same for each trial.
V. All outcomes in the sample space are equally likely

Part 2: Free Response

Show all your work. Indicate clearly the methods you use, because you will be graded on the correctness of your methods as well as on the accuracy and completeness of your results and explanations.

Picard Partners is planning a major investment. The amount of profit X is uncertain but a probabilistic estimate gives the following distribution (in millions of dollars)

2

Find and interpret the mean of X.

2

Find and interpret the Standard Deviation of X.

2

Picard owes its source of capital a fee of $200,000 plus 10% of the profits X. So the firm actually retains Y = 0.9X – 0.2 from the investment. Use a linear transformation of your results in (a) and (b) to find the mean and standard deviation for Y

Witney Pete, a professional dart player, has a 70% chance of hitting the bull’s eye on a dartboard with any throw. Assume that each throw of a dart is independent.

1

Suppose Pete throws darts until he hits his first bull’s eye. Find the probability that his first bull’s eye occurs on the third throw.

1

What is the probability that Pete hits 5 or fewer of his next 10 shots

1

In the United States, 44% of adults have type O blood. Suppose we choose 7 U.S. adults at random. Let X= the number of people who have type O blood. Use the binomial probability formula to find P(X=4). Interpret your answer in the context of the problem.

1

How surprising would it be to get more than 4 adults with type O blood in the sample? Calculate an appropriate probability to support your answer. Make sure to explain clearly and show all your work.

Chapter 6 Practice Test

Chapter 6 Practice Test

Classify each variable as a discrete or continuous random variable

In a probability distribution, the Probability must satisfy which two requirements?

What is the expected value of X?

Suppose that the distribution of a set of scores has a mean of 47 and a standard deviation of 14. If 4 is added to each score, what will be the mean and the standard deviation of the distribution of new scores?

Roll one 8-sided die 10 times. The probability of getting exactly 3 sevens in those 10 rolls is given by

Let the random variable X represent the profit made on a randomly selected day by a certain store. Assume that X is Normal with mean $360 and standard deviation $50. What is P(X > $400)?

A dealer in the Sands Casino in Las Vegas selects 40 cards from a standard deck of 52 cards. Let Y be the number of red cards (hearts or diamonds) in the 40 cards selected. Which of the following best describes this setting

In a large population of college students, 20% of the students have experienced feelings of math anxiety. If you take a random sample of 10 students from this population, the mean and standard deviation of the number of students in the sample who have experienced math anxiety is:

Which of the following is a true statement?

Find and interpret the mean of X.

Find and interpret the Standard Deviation of X.

Picard owes its source of capital a fee of $200,000 plus 10% of the profits X. So the firm actually retains Y = 0.9X – 0.2 from the investment. Use a linear transformation of your results in (a) and (b) to find the mean and standard deviation for Y

Suppose Pete throws darts until he hits his first bull’s eye. Find the probability that his first bull’s eye occurs on the third throw.

What is the probability that Pete hits 5 or fewer of his next 10 shots

In the United States, 44% of adults have type O blood. Suppose we choose 7 U.S. adults at random. Let X= the number of people who have type O blood. Use the binomial probability formula to find P(X=4). Interpret your answer in the context of the problem.

How surprising would it be to get more than 4 adults with type O blood in the sample? Calculate an appropriate probability to support your answer. Make sure to explain clearly and show all your work.

Classify each variable as a discrete or continuous random variable

In a probability distribution, the Probability must satisfy which two requirements?

What is the expected value of X?

Suppose that the distribution of a set of scores has a mean of 47 and a standard deviation of 14. If 4 is added to each score, what will be the mean and the standard deviation of the distribution of new scores?

Roll one 8-sided die 10 times. The probability of getting exactly 3 sevens in those 10 rolls is given by

Let the random variable X represent the profit made on a randomly selected day by a certain store. Assume that X is Normal with mean $360 and standard deviation $50. What is P(X > $400)?

A dealer in the Sands Casino in Las Vegas selects 40 cards from a standard deck of 52 cards. Let Y be the number of red cards (hearts or diamonds) in the 40 cards selected. Which of the following best describes this setting

In a large population of college students, 20% of the students have experienced feelings of math anxiety. If you take a random sample of 10 students from this population, the mean and standard deviation of the number of students in the sample who have experienced math anxiety is:

Which of the following is a true statement?

Find and interpret the mean of X.

Find and interpret the Standard Deviation of X.

Picard owes its source of capital a fee of $200,000 plus 10% of the profits X. So the firm actually retains Y = 0.9X – 0.2 from the investment. Use a linear transformation of your results in (a) and (b) to find the mean and standard deviation for Y

Suppose Pete throws darts until he hits his first bull’s eye. Find the probability that his first bull’s eye occurs on the third throw.

What is the probability that Pete hits 5 or fewer of his next 10 shots

In the United States, 44% of adults have type O blood. Suppose we choose 7 U.S. adults at random. Let X= the number of people who have type O blood. Use the binomial probability formula to find P(X=4). Interpret your answer in the context of the problem.

How surprising would it be to get more than 4 adults with type O blood in the sample? Calculate an appropriate probability to support your answer. Make sure to explain clearly and show all your work.