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Chapter 6: Q.11 (page 354)

Spell-checking Refer to Exercise 3. Calculate the mean of the random variable X and interpret this result in context.

Short Answer

Expert verified

On average there are 2.1 nonword errors in a 250-word essay.

Step by step solution

01

Given Information

The number X of nonword errors has the following distribution:

02

Explanation

The sum of each alternative multiplied by its likelihood is the expected value:

E(X)=鈭�xP(x)=0脳0.1+1脳0.2+2脳0.3+3脳0.3+4脳0.1=2.1

This suggests that in a 250-word essay, there are on average 2.1 nonword errors.

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Most popular questions from this chapter

90. Normal approximation To use a Normal distribution to approximate binomial probabilities, why do we require that both np and n(1鈭�p) be at least 10?

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.

20. Size of American households In government data, a household consists of all occupants of a dwelling unit, while a family consists of two or more persons who live together and are related by blood or marriage. So all families form households, but some households are not families. Here are the distributions of household size and family size in the United States:

Let X = the number of people in a randomly selected U.S. household and Y = the number of people in a randomly chosen U.S. family.
(a) Make histograms suitable for comparing the probability distributions of X and Y. Describe any differences that you observe.
(b) Find the mean for each random variable. Explain why this difference makes sense.
(c) Find the standard deviations of both X and Y. Explain why this difference makes sense.

The length in inches of a cricket chosen at random from a field is a random variable Xwith mean 1.2inches and standard deviation of 0.25 inches. Find the mean and standard deviation of the length Y of a randomly chosen cricket from the field in centimeters. There are 2.54 centimeters in an inch.

49. Checking independence In which of the following games of chance would you be willing to assume independence of Xandlocalid="1649903939419" Y in making a probability model? Explain your answer in each case.
(a) In blackjack, you are dealt two cards and examine the total points localid="1649903945891" Xon the cards (face cards count localid="1649903950298" 10points). You can choose to be dealt another card and compete based on the total pointslocalid="1649903956461" Y on all three cards.
(b) In craps, the betting is based on successive rolls of two dice. localid="1649903966379" Xis the sum of the faces on the first roll, and localid="1649903971075" Yis the sum of the faces on the next roll.
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