Statistics Quiz

28 Jun Statistics Quiz

1.An economist says that the probability is 0.47 that a randomly selected adult is in favor of keeping the Social Security system as it is, 0.32 that this adult is in favor of totally abolishing the Social Security system, and 0.21 that this adult does not have any opinion or is in favor of other options. Were these probabilities obtained using the classical approach, relative frequency approach, or the subjective probability approach?

A. Classical probability approach.

B. Relative frequency approach.

C. Subjective probability approach.

2. In a sample of 300 adults, 111 like chocolate ice cream and 96 like vanilla ice cream. One adult is randomly selected from these adults. Round your answer to 2 decimal places.

a. What is the probability that this adult likes chocolate ice cream?

Probability =

b. What is the probability that this adult likes vanilla ice cream?

Probability =

c. Do these two probabilities add to 1.0?

3. In a sample of 500 families, 50 have a yearly income of less than $50,000, 210 have a yearly income of $ 50,000 to $ 100,000, and the remaining families have a yearly income of more than $ 100,000.

Write the frequency distribution table for this problem. Calculate the relative frequencies for all classes.

Income Frequency Relative

Less than 50k

50k to 100K

More than 100K

Suppose one family is randomly selected from these 500 families. Find the probability that this family has a yearly income of less than $ 50,000.

P(income is less than $ 50,000)=

b. Suppose one family is randomly selected from these 500 families. Find the probability that this family has a yearly income of more than $ 100,000.

P(income is more than $ 100,000)=

4. Classify the following random variable as discrete or continuous.

The time left on a parking meter.

5. Classify the following random variable as discrete or continuous.

The number of bats broken by a major league baseball team in a season.

6. The following table lists certain values of x and their probabilities. Verify whether or not it represents a valid probability distribution.

X p(x)

0 0.36

1 0.30

2 0.19

3 0.12

The table (does or does not represent) a valid probability distribution?

7. The following table gives the probability distribution of a discrete random variable x.

X 0 1 2 3 4 5 6

P(x) 0.12 0.19 0.29 0.15 0.12 0.07 0.06

Find P(x≥4).

P(x≥4)=

8. The following table gives the probability distribution of a discrete random variable x.

X 0 1 2 3 4 5 6

P(x) 0.11 0.20 0.28 0.15 0.12 0.07 0.07

Find P(x≥2).

P(x≥2)=

9. . The following table gives the probability distribution of a discrete random variable x.

X 0 1 2 3 4 5 6

P(x) 0.13 0.19 0.30 0.15 0.12 0.09 0.02

Find P(1≤x≤4).

P(1≤x≤4)=

10. Find the mean and standard deviation for the following probability distribution.

X P(x)

6 0.38

7 0.23

8 0.22

9 0.17

Enter the exact answer for the mean and round the standard deviation to three decimal places.

Mean =

Standard deviation =

11. Which of the following are binomial experiments?

a. Rolling a die many times and observing the number of spots. Binomial or Non

b. Rolling a die many times and observing whether the number obtained is even or odd. Binomial or Non

c. Selecting a few voters from a very large population of voters and observing whether or not each of them favors a certain proposition in an election when 54% of all voters are known to be in favor of this proposition. Binomial or Non

12. According to a survey, 75% of households said that they have never purchased organic fruits or vegetables. Suppose that this result is true for the current population of households.

a. Let x be a binomial random variable that denotes the number of households in a random sample of 10 who have never purchased organic fruits or vegetables. What are the possible values that x can assume?

Integers ( ) to ( ).

b. Find to 3 decimal places the probability that exactly 6 households in a random sample of 10 will say that they have never purchased organic fruits or vegetables. Use the binomial probability distribution formula.