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Chapter 6: Q. 2.2 (page 390)

To introduce her class to binomial distributions, Mrs. Desai gives a 10-item, multiple choice quiz. The catch is, students must simply guess an answer (A through E) for each question. Mrs. Desai uses her computer's random number generator to produce the answer key, so that each possible answer has an equal chance to be chosen. Patti is one of the students in this class. Let X=the number of Patti's correct guesses.

Find P(X=3). Explain what this result means.

Short Answer

Expert verified

The value ofP(X=3)is0.2013

Step by step solution

01

Given Information 

Number of questions=10

Students are supposed to guess the answers.

Xis a number of answers that Patti gives correct.

02

Explanation

The binomial distribution pdf is:

P(X=r)=Crn×pr×(1-p)r

Calculation:

Using Ti-83 plus calculator P(X=3)can be calculated as:

Thus, 0.213is the required probability

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Most popular questions from this chapter

Ms. Hall gave her class a 10-question multiple-choice quiz. Let X=the number of questions that a randomly selected student in the class answered correctly. The computer output below gives information about the probability distribution of X. To determine each student’s grade on the quiz (out of 100), Ms. Hall will multiply his or her number of correct answers by 10. Let G=the grade of a randomly chosen student in the class.

NMeanMedianStDevMinMaxQ1Q3307.68.51.3241089

(a) Find the median of G. Show your method.

(b) Find the IQR of G. Show your method.

(c) What shape would the probability distribution of Ghave? Justify your answer

Kids and toys Refer to Exercise 4. Calculate and interpret the standard deviation of the random variable X. Show your work.

Days01234567Probability0.680.050.070.080.050.040.010.02

Working out Refer to Exercise 6. Consider the events A = works out at least once and B = works out less than 5 times per week.

(a) What outcomes makeup event A? What is P(A)?

(b) What outcomes make up event B? What is P(B)?

(c) What outcomes make up the event “A and B”? What is P(A and B)? Why is this probability not equal to P(A) · P(B)?

Keno is a favorite game in casinos, and similar games are popular in the states that operate lotteries. Balls numbered 1to 80are tumbled in a machine as the bets are placed, then 20of the balls are chosen at random. Players select numbers by marking a card. The simplest of the many wagers available is “Mark 1Number.” Your payoff is 3on a bet if the number you select is one of those chosen. Because 20of 80numbers are chosen, your probability of winning is 20/80, or 0.25. Let X=the amount you gain on a single play of the game.

(a) Make a table that shows the probability distribution of X.

(b) Compute the expected value of X. Explain what this result means for the player

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 first hour of business on a randomly selected Friday. Based on previous records, the probability distributions of Xand Yare as follows:

Define D=X-Y.

The dealership’s manager receives a 500bonus for each car sold and a300 bonus for each car leased. Find the mean and standard deviation of the difference in the manager’s bonus for cars sold and leased. Show your work.
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