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Chapter 6: Q. 52 (page 358)

Sul茅鈥檚 job is just a few bus stops away from his house. While it can be faster to take the bus to work than to walk, the travel time is more variable due to traffic. The commute time B if Sul茅 takes the bus to work on a randomly selected day has mean 12 minutes and standard deviation 4 minutes. The commute time W if Sul茅 walks to work on a randomly selected day has mean 16 minutes and standard deviation 1 minute. Calculate and interpret the mean of the difference D=B鈭�W in the time it would take Sul茅 to get to work on a randomly selected day?

Short Answer

Expert verified

The resultant difference of mean is渭=鈭�4

Step by step solution

01

Given information

渭B=12蟽B=4渭W=16蟽W=1

B=Bus commuting time

W=when conversing on the way to work

02

Calculations

渭=渭B鈭�渭W=12鈭�16=鈭�4

Because there are two means for two different random variables 渭B=12 and 渭W=16, the mean of the two random variables will be the difference of their means, resulting in a commute time by bus that is on average 4 minutes less than a commute by walking.

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Most popular questions from this chapter

Lefties A total of 11%of students at a large high school are left-handed. A statistics teacher selects a random sample of 100 students and records L= the number of left-handed students in the sample.

a. Explain why L can be modeled by a binomial distribution even though the sample was selected without replacement.

b. Use a binomial distribution to estimate the probability that 15 or more students in the sample are left-handed.

Long or short? Put the names of all the students in your statistics class in a hat. Mix up the names, and draw 4 without looking. Let X = the number whose last names have more than six letters.

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

Geometric or not? Determine whether each of the following scenarios describes a geometric setting. If so, define an appropriate geometric random variable.

a. Shuffle a standard deck of playing cards well. Then turn over one card at a time from the top of the deck until you get an ace.

b. Billy likes to play cornhole in his free time. On any toss, he has about a 20%chance of getting a bag into the hole. As a challenge one day, Billy decides to keep tossing bags until he gets one in the hole.

Spell-checking Spell-checking software catches 鈥渘onword errors,鈥� which result in a string of letters that is not a word, as when 鈥渢he鈥� is typed as 鈥渢eh.鈥� When undergraduates are asked to write a 250-word essay (without spell-checking), the number Y of nonword errors in a randomly selected essay has the following probability distribution

Part (a). Write the event 鈥渙ne nonword error鈥� in terms of Y. Then find its probability.

Part (b). What鈥檚 the probability that a randomly selected essay has at least two nonword errors?
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