1. In the population of children in grade 5 in the United States, 25% score belo

Question

1. In the population of children in grade 5 in the United States, 25% score below 5.0 on a math test. Marjorie obtains a random sample of 102 grade 5 children. What is the probability that the mean of this sample will be less than 5.0?

a. 100%

b. less than 25%

c. more than 25% but less than 100%

d. 25%

2. The central limit theorem describes the distribution of means when

a. the sample size is small

b. the parent population is small

c. the parent population is large

d. the sample size is large

3. When the sample size is large enough, the distribution of means will be normal if_____

a. the population is normal

b. the population is bimodal

c. the population is skewed

d. all of the above

e. none of the above

4. If the parent population has a mean of 50 and standard deviation of 10, then the distribution of the means will have a standard error that is

a. less than 10

b. more than 50

c. less than 50

d. more than 10

5. In the population, 16% of adults score above 60 on the Extraversion Test. Dr. Goldberg obtains a random sample of 500 adults. What is the probability that the mean of this sample will be greater than 60?

a. 16%

b. more than 16%

c. more than 16% but less than 32%

d. less than 16%

6. Juice bottles are designed to contain 8 oz of fluid. Customers get angry when the bottles contain less than 7.6 oz. In one factory, 3% of the bottles have less than 7.6 oz. However, the juice bottles are sold in packages that contain 6 bottles. In this same factory, we calculate the average volume in each package. What is the probability that a package will have an average volume that is less than 7.6 oz?

a. more than 3%

b. 3%

c. less than 3%

Explanation / Answer

1. In the population of children in grade 5 in the United States, 25% score below 5.0 on a math test. Marjorie obtains a random sample of 102 grade 5 children. What is the probability that the mean of this sample will be less than 5.0?

Answer : Here p = 0.25

so probability that the mean of this sample will be less than 5.0 will be 25% (option D)

2. The central limit theorem describes the distribution of means when the sample size is large, (option D)

3. When the sample size is large enough, the distribution of means will be normal if " all of the above" (option D)

distribution of means will be normal in every case when population is normal, bimodal or skewed.

4. If the parent population has a mean of 50 and standard deviation of 10, then the distribution of the means will have a standard error that is

Standard error of mean = standard deviation of population/ n

so standard error of the mean < standard deviation of population < less than 10

so, option a is correct.

5. In the population, 16% of adults score above 60 on the Extraversion Test. Dr. Goldberg obtains a random sample of 500 adults. What is the probability that the mean of this sample will be greater than 60?

Answer : The probability that the mean of this sample will be greater than 60 will be equal to 16%. [ Option a]

6. Juice bottles are designed to contain 8 oz of fluid. Customers get angry when the bottles contain less than 7.6 oz. In one factory, 3% of the bottles have less than 7.6 oz. However, the juice bottles are sold in packages that contain 6 bottles. In this same factory, we calculate the average volume in each package. What is the probability that a package will have an average volume that is less than 7.6 oz?

Ans. That is the same type of question, so probability that a package will have an average volume that is less than 7.6 oz is equal to 3%. [ Option B]

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