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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

Most states and Canadian provinces have government-sponsored lotteries. Here is a simple lottery wager, from the Tri-State Pick 3game that New Hampshire shares with Maine and Vermont. You choose a number with 3digits from 0to 9; the state chooses a three-digit winning number at random and pays you \(500if your number is chosen. Because there are 1000numbers with three digits, you have a probability of 1/1000of winning. Taking Xto be the amount your ticket pays you, the probability distribution of Xis

(a) Show that the mean and standard deviation of Xare 渭X=\)0.50and 蟽X=\(15.80.

(b) If you buy a Pick 3 ticket, your winnings are W=X-1, because it costs \)1to play. Find the mean and standard deviation of W. Interpret each of these values in context.

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?

Based on the analysis in Exercise 41, the ferry company decides to increase the cost of a trip to $6. We can calculate the company鈥檚 profit Yon a randomly selected trip from the number of cars X. Find the mean and standard deviation ofY. Show your work.

54. The Tri -State Pick 3Refer to Exercise 42. Suppose 365
(a) Find the mean and standard deviation of your total winnings. Show your work.
(b) Interpret each of the values from (a) in context .

83. Random digit dialing Refer to Exercise 81. Let Y= the number of calls that don鈥檛 reach a live person.

(a) Find the mean of Y. How is it related to the mean of X? Explain why this makes sense.
(b) Find the standard deviation of Y.How is it related to the standard deviation of X? Explain why this makes sense

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