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Chapter 6: Q. 3.3 (page 393)

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.

Short Answer

Expert verified

Patti's correct estimates had a 0.322 chance of being more than2 standard deviations above the mean.

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.

Probability of success(p)=0.2

02

Explanation 

We can compute the probability of more than 2correct answers by using the formula below, :

P(X>2)=鈭�r=210Cr10脳(0.2)r脳(1-0.2)10-r=0.322.

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Most popular questions from this chapter

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.

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

21. Random numbers Let Xbe a number between 0and 1produced by a random number generator. Assuming that the random variable X has a uniform distribution, find the following probabilities:
(a) P(X>0.49)
(b) P(X鈮�0.49)
(c) P(0.19鈮�X<0.37or0.84<X鈮�1.27)

19. Housing in San Jose How do rented housing units differ from units occupied by their owners? Here are the distributions of the number of rooms for owner-occupied units and renter-occupied units in San Jose,
California:

Let X = the number of rooms in a randomly selected owner-occupied unit and Y = the number of rooms in a randomly chosen renter-occupied unit.
(a) Make histograms suitable for comparing the probability distributions of X and Y. Describe any differences that you observe.
(b) Find the mean number of rooms for both types of housing unit. Explain why this difference makes sense.
(c) Find the standard deviations of both X and Y. Explain why this difference makes sense.

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.

1. Find 渭X. Interpret this value in context.
See all solutions

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