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Chapter 6: Q. 50 (page 389)

Typographical and spelling errors can be either 鈥渘onword errors鈥� or 鈥渨ord errors.鈥� A nonword error is not a real word, as when 鈥渢he鈥� is typed as 鈥渢eh.鈥� A word error is a real word, but not the right word, as when 鈥渓ose鈥� is typed as 鈥渓oose.鈥� When students are asked to write a 250-word essay (without spell-checking), the number of nonword errors X in a randomly selected essay has mean 2.1 and standard deviation 1.136. The number of word errors Y in the essay has mean 1.0 and standard deviation 1.0. Calculate and interpret the mean of the sum S = X + Y.

Short Answer

Expert verified

The Average mean value is渭=3.1

Step by step solution

01

Given information

The number of nonword errors X in a randomly selected essay has mean 2.1 and standard deviation 1.136

The number of word errors X in a randomly selected essay has mean 1.0 and standard deviation 1.0

渭X=2.1蟽X=1.136渭Y=1.0蟽Y=1.0

X = quantity of nonword errors in an essay chosen at random

Y= quantity of word errors in an essay chosen at random

02

Calculations

渭=渭X+渭Y=2.1+1.0=3.1

There are two different random variables with two different means,渭X=2.1and 渭Y=1.0

as a result, the average of the two random numbers ,the total of their means will be the variable.

On average, there will be a total number of 3.1 errors

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Most popular questions from this chapter

Quick, click! An Internet reaction time test asks subjects to click their mouse button as soon as a light flashes on the screen. The light is programmed to go on at a randomly selected time after the subject clicks 鈥淪tart.鈥� The density curve models the amount of time Y (in seconds) that the subject has to wait for the light to flash.

a) Find and interpret P(Y>3.75)

b) What is 渭Y? Explain your answer.

c) Find the value of k that makes this statement true:P(Y鈮�k)=0.38

Red light! Pedro drives the same route to work on Monday through Friday. His route includes one traffic light. According to the local traffic department, there is a 55%chance

that the light will be red on a randomly selected work day. Suppose we choose 10 of Pedro's work days at random and let Y= the number of times that the light is red. Make a graph of the probability distribution of Y . Describe its shape.

Working outExercise 10 described a large sample survey that asked a sample of people aged 19 to 25 years, 鈥淚n the past seven days, how many times did you go to an exercise or fitness center or work out?鈥� The response Y for a randomly selected survey respondent has the probability distribution shown here. From Exercise 10, E(Y)=1.03. Find the standard deviation of Y. Interpret this value.

Taking the train Refer to Exercise 80 . Use the binomial probability formula to find P(Y=4). Interpret this value.

In which of the following situations would it be appropriate to use a Normal distribution to approximate probabilities for a binomial distribution with the given values of n and p ?

a. n=10,p=0.5

b. n=40,p=0.88

c. n=100,p=0.2

d. n=100,p=0.99

e.n=1000,p=0.003
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