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Chapter 6: Q. 2.3 (page 390)

To introduce her class to binomial distributions, Mrs. Desai gives a 10-item, multiple-choice quiz. The catch is, that 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.

To get a passing score on the quiz, a student must guess correctly at least 6times. Would you be surprised if Patti earned a passing score? Compute an appropriate probability to support your answer.

Short Answer

Expert verified

The probability is0.0064.

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脳pr脳(1-p)r

Calculation:

Using Ti-83 plus calculator P(X<6)can be calculated as:

Now,P(X鈮�6)can be calculated as

localid="1649855112536" P(X鈮�6)=1鈭�P(X<6)=1鈭�0.9936=0.0064

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Most popular questions from this chapter

What鈥檚 the expected number of cars in a randomly selected American household?

(a) Between 0and 5

(b) 1.00

(c) 1.75

(d) 1.84

(e) 2.00

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.

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 蟿=蠂+纬

The dealership鈥檚 manager receives a 500bonus for each car sold and a 300 bonus for each car leased. Find the mean and standard deviation of the manager鈥檚 total bonus B. Show your work.

Rotter Partners is planning a major investment. The amount of profit X(in millions of dollars) is uncertain, but an estimate gives the following probability distribution:

Based on this estimate, 渭X=3and 蟽X=2.52

Rotter Partners owes its lender a fee of $200,000plus 10%of the profits X. So the firm actually retains Y=0.9X-0.2from the investment. Find the mean and standard deviation of the amount Ythat the firm actually retains from the investment.

Ten lines in the table contain 400digits. The count of 0s in these lines is approximately Normal with

(a) mean 40; standard deviation 36.

(b) mean 40; standard deviation19.

(c) mean 40; standard deviation 6.

(d) mean 36; standard deviation6.

(e) mean 10; standard deviation 19.
See all solutions

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