8.4 - Test Yourself!

Question 1

A die is rolled 6 times. Which of the following is the most likely sequence of rolls?

3,1,4,2,6,4
All possibilities are equally likely on each roll so no number is more likely than another regardless of how previous rolls turn out.
2,2,2,2,2,2
All possibilities are equally likely on each roll so no number is more likely than another regardless of how previous rolls turn out.
1,2,3,4,5,6
All possibilities are equally likely on each roll so no number is more likely than another regardless of how previous rolls turn out.
All of the above are equally likely
Correct. All possibilities are equally likely on each roll so no number is more likely than another regardless of how previous rolls turn out.

Question 2

Which of these will follow the normal curve most closely?

The histogram of the household incomes from a census of all of the households in Pennsylvania.
The answer is: A histogram of all of the possible sample means from samples of 100 household incomes in Pennsylvania. The population histogram (situation A) is likely to be very skewed to the right and the histogram of the sample data (situation B) is likely to reflect that. The sampling distribution of the mean will look very much like the normal curve – especially for a larger sample (situation C).
The histogram of the household incomes from a sample of 100 households in Pennsylvania.
The answer is: A histogram of all of the possible sample means from samples of 100 household incomes in Pennsylvania. The population histogram (situation A) is likely to be very skewed to the right and the histogram of the sample data (situation B) is likely to reflect that. The sampling distribution of the mean will look very much like the normal curve – especially for a larger sample (situation C).
A histogram of all of the possible sample means from samples of 100 household incomes in Pennsylvania.
Correct. The population histogram (situation A) is likely to be very skewed to the right and the histogram of the sample data (situation B) is likely to reflect that. The sampling distribution of the mean will look very much like the normal curve – especially for a larger sample (situation C).
A histogram of all of the possible sample means from samples of 5 household incomes in Pennsylvania.
The answer is: A histogram of all of the possible sample means from samples of 100 household incomes in Pennsylvania. The population histogram (situation A) is likely to be very skewed to the right and the histogram of the sample data (situation B) is likely to reflect that. The sampling distribution of the mean will look very much like the normal curve – especially for a larger sample (situation C).

Question 3

A company matches employee contributions to a retirement fund up to $10,000 per year. A histogram of the cost for each employee is left skewed (since most employees get close to the maximum but a few do not take advantage of the program). Despite this fact,

the distribution of the average cost for a randomly selected group of 50 employees would still follow the normal curve.

Correct. The sampling distribution for a sample of size 50 should be very well approximated by a normal distribution.
the distribution of the cost for a randomly selected employee would still follow the normal curve.

The answer is: The distribution of the average cost for a randomly selected group of 50 employees would still follow the normal curve. The sampling distribution for a sample of size 50 should be very well approximated by a normal distribution.
neither distribution would follow the normal curve.

The answer is: The distribution of the average cost for a randomly selected group of 50 employees would still follow the normal curve. The sampling distribution for a sample of size 50 should be very well approximated by a normal distribution.

Question 4

The average amount spent by customers that attend a New Years Eve party at a restaurant and bar is $83 with a standard deviation of $60. You would expect that a sample of 25 of these customers would spend an average of $83 with a standard deviation of?

$$60$
The answer is: $$12$. The standard deviation for the sample mean will be the population standard deviation divided by the square root of the sample size = $$60 / 5 = $12$.
$$12$
Correct. The standard deviation for the sample mean will be the population standard deviation divided by the square root of the sample size = $$60 / 5 = $12$.
$$83$
The answer is: $$12$. The standard deviation for the sample mean will be the population standard deviation divided by the square root of the sample size = $$60 / 5 = $12$.
$$2.40$
The answer is: $$12$. The standard deviation for the sample mean will be the population standard deviation divided by the square root of the sample size = $$60 / 5 = $12$.

Question 5

The chance that a certain type of thumbtack lands point up when you toss it in the air is 80%. This makes the standard deviation of the proportion of times it lands point up out of 100 tosses equal to?

0.4
The correct answer is $\sqrt{0.8(0.2)/100} = 0.04$.
0.8
The correct answer is $\sqrt{0.8(0.2)/100} = 0.04$.
0.04
Correct. $\sqrt{0.8(0.2)/100} = 0.04$.
0.008
The correct answer is $\sqrt{0.8(0.2)/100} = 0.04$.

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8.4 - Test Yourself!

Think About It!