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Chapter 7: Q 40. (page 462)

Scrabble In the game of Scrabble, each player begins by drawing 7 tiles from a bag

containing 100 tiles. There are 42 vowels, 56 consonants, and 2 blank tiles in the bag. Cait chooses an SRS of 7 tiles. Let p^ be the proportion of vowels in her sample.

a. Is the 10% condition met in this case? Justify your answer.

b. Is the Large Counts condition met in this case? Justify your answer.

Short Answer

Expert verified

a. Yes.

b. No, large count condition is not met.

Step by step solution

01

Given Information

It is given that number of vowels is42and number of tiles are100.

02

Do 10% condition met in this case

Yes, it is met as7<10%of population size of100.

03

Do large count condition met

Population proportion is calculated as:

p=Population proportion=Number of vowelsNumber of tiles=42100=0.42

and n=7

Condition of normality is np鈮�10andn(1-p)鈮�10

Now, np=7(0.42)=2.94<10

and

n(1-p)=7(1-0.42)=4.06<10

Hence, large counts condition is not satisfied.

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Most popular questions from this chapter

A 10-question multiple-choice exam offers 5 choices for each question. Jason just guesses the answers, so he has probability 15of getting any one answer correct. You want to perform a simulation to determine the number of correct answers that Jason gets. What would be a proper way to use a table of random digits to do this?

a. One digit from the random digit table simulates one answer, with 5 = correct and all other digits = incorrect. Ten digits from the table simulate 10 answers.

b. One digit from the random digit table simulates one answer, with 0 or 1 = correct and all other digits = incorrect. Ten digits from the table simulate 10 answers.

c. One digit from the random digit table simulates one answer, with odd = correct and even = incorrect. Ten digits from the table simulate 10 answers.

d. One digit from the random digit table simulates one answer, with 0 or 1 = correct and all other digits = incorrect, ignoring repeats. Ten digits from the table simulate 10 answers.

e. Two digits from the random digit table simulate one answer, with 00 to 20 = correct and 21 to 99 = incorrect. Ten pairs of digits from the table simulate 10 answers.

The central limit theorem is important in statistics because it allows us to use a Normal distribution to find probabilities involving the sample mean if the

a. sample size is reasonably large (for any population).

b. population is Normally distributed (for any sample size).

c. population is Normally distributed and the sample size is reasonably large.

d. population is Normally distributed and the population standard deviation is known (for any sample size).

e. population size is reasonably large (whether the population distribution is known or not).

The manufacturer of a certain brand of aluminum foil claims that the amount of foil on each roll follows a Normal distribution with a mean of 250 square feet (ft2 ) and a standard deviation of 2 ft2 . To test this claim, a restaurant randomly selects 10 rolls of this aluminum foil and carefully measures the mean area to bex=249.6ft2.

a. Find the probability that the sample mean area is 249.6ft2or less if the manufacturer鈥檚 claim is true.

b. Based on your answer to part (a), is there convincing evidence that the company is overstating the average area of its aluminum foil rolls?

Cereal A company's cereal boxes advertise that each box contains 9.65 ounces of cereal. In fact, the amount of cereal in a randomly selected box follows a Normal distribution with mean 渭=9.70 ounces and standard deviation 蟽=0.03 ounce.

a. What is the probability that a randomly selected box of the cereal contains less than 9.65 ounces of cereal?

b. Now take an SRS of 5 boxes. What is the probability that the mean amount of cereal in these boxes is less than 9.65 ounces?

Airline passengers get heavier In response to the increasing weight of airline passengers, the Federal Aviation Administration (FAA) told airlines to assume that passengers average 190 pounds in the summer, including clothes and carry-on baggage. But passengers vary, and the FAA did not specify a standard deviation. A reasonable standard deviation is 35 pounds. A commuter plane carries 30 passengers. Find the probability that the total weight of 30 randomly selected passengers exceeds 6000 pounds.
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