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Chapter 6: Q. 9 (page 409)

T6.9. The figure shows the probability distribution of a discrete random variable X. Which of the following best describes this random variable?

(a) Binomial withn=8,p=0.1
(b) Binomial with n = 8, p = 0.3
(c) Binomial withn=8,p=0.8
(d) Geometric withp=0.1
(e) Geometric with p = 0.2

Short Answer

Expert verified

Binomial with n = 8, p = 0.3. So, the option(b) is correct.

Step by step solution

01

Given information

The probability distribution of a discrete random variable X. To find the random variable in the given figure.

02

Explanation

a geometric distribution is known as a binomial distribution. Because the largest bar in the following histogram is at X=1
The probability determined by:
P(X=7)=0.001224withn=8.
Calculate the probabilityp :
binompdf(8,0.1,7)=0.00000072
binompdf(8,0.3,7)=0.00122472
binompdf(8,0.8,7)=0.33554432
Note that: p=0.3, then the probability matches the probability in the calculator.

So, the option(b) is correct.

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Most popular questions from this chapter

Refer to the previous Check Your Understanding (page 390) about Mrs. Desai's special multiple-choice quiz on binomial distributions. We defined X=the number of Patti's correct guesses.

3. What's the probability that the number of Patti's correct guesses is more than 2standard deviations above the mean? Show your method.

A deck of cards contains 52cards, of which 4are aces. You are offered the following wager: Draw one card at random from the deck. You win \(10if the card drawn is an ace. Otherwise, you lose \)1. If you make this wager very many times, what will be the mean amount you win?

(a) About 鈭�\(1, because you will lose most of the time.

(b) About \)9, because you win \(10but lose only \)1.

(c) About 鈭�\(0.15; that is, on average you lose about 15cents. (d) About \)0.77; that is, on average you win about 77cents.

(e) About $0, because the random draw gives you a fair bet.

86.1in 6wins As a special promotion for its 20-ounce bottles of soda, a soft drink company printed a message on the inside of each cap. Some of the caps said, 鈥淧lease try again,鈥� while others said, 鈥淵ou鈥檙e a winner!鈥� The company advertised the promotion with the slogan 鈥�1in6wins a prize.鈥� Suppose the company is telling the truth and that every 20-ounce
bottle of soda it fills has a1-in-6chance of being a winner. Seven friends each buy one 20-ounce bottle of the soda at a local convenience store. Let X= the number who win a prize.
(a) Explain why X is a binomial random variable.
(b) Find the mean and standard deviation of X. Interpret each value in context.

(c) The store clerk is surprised when three of the friends win a prize. Is this group of friends just lucky, or is the company鈥檚 1-in-6 claim inaccurate? Compute P(X鈮�3) and use the result to justify your answer.

A large auto dealership keeps track of sales and leases agreements made during each hour of the day. Let X= the number of cars sold and Y= the number of cars leased during the 铿乺st hour of business on a randomly selected Friday. Based on previous records, the probability distributions of Xand Yare as follows:

顿别铿乶别 T=X+Y.

Find and interpret 渭T.

Toss 4times Suppose you toss a fair coin 4times. Let X=the number of heads you get.

(a) Find the probability distribution ofX.

(b) Make a histogram of the probability distribution. Describe what you see.

(c) Find P(X鈮�3) and interpret the result.
See all solutions

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