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# MATH 302 MIDTERM EXAM 2 – QUESTION AND ANSWERS|AMERICAN PUBLIC UNIVERSITY

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**MATH 302 Midterm Exam 2 Question and Answers**

**PART 1 OF 9**

1. Which measure of central location is meaningful when the data are categorical?

2. What type of probability uses sample spaces to determine the numerical probability that an event will occur?

3. The formal way to revise probabilities based on new information is to use:

**PART 3 OF 9**

4. Suppose that 50 identical batteries are being tested. After 8 hours of continuous use, assume that a given battery is still operating with a probability of 0.70 and has failed with a probability of 0.30.

5. Find the variance of the following probability distribution.

6. Which term is NOT synonymous with the expected value of a discrete probability distribution?

**PART 4 OF 9**

7. Given that Z is a standard normal random variable, P(-1.0 < Z < 1.5) is

8. The continuous distribution characterized by a symmetric, bell-shaped curve is the:

9. The standard deviation of a probability distribution must be:

10. Given that Z is a standard normal variable, the value z for which P(Z < z) = 0.2580 is

11. The standard normal distribution has a mean of ___ and standard deviation of ___, respectively.

12. One reason for standardizing random variables is to measure variables with:

**PART 5 OF 9**

13. Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), “E” or “e” (used in scientific notation). Complex numbers should be in the form (a + bi) where “a” and “b” need to have explicitly stated values.

For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not. The following data represent the number of children in a sample of 10 families from Chicago: 4, 2, 1, 1, 5, 3, 0, 1, 0, and 2. Compute the variance of the data. Place your answer, rounded to two decimal places, in the blank.

**PART 6 OF 9**

14. Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), “E” or “e” (used in scientific notation). Complex numbers should be in the form (a + bi) where “a” and “b” need to have explicitly stated values.

For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not.

15. Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), “E” or “e” (used in scientific notation). Complex numbers should be in the form (a + bi) where “a” and “b” need to have explicitly stated values.

For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not. The following data were obtain from a survey of college students. The variable X represents the number of non-assigned books read during the past six months.

**PART 7 OF 9**

16. Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), “E” or “e” (used in scientific notation). Complex numbers should be in the form (a + bi) where “a” and “b” need to have explicitly stated values.

For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not.

An ice cream vendor sells three flavors: chocolate, strawberry, and vanilla. Forty five percent of the sales are chocolate, while 30% are strawberry, with the rest vanilla flavored. Sales are by the cone or the cup. The percentages of cones sales for chocolate, strawberry, and vanilla, are 75%, 60%, and 40%, respectively. For a randomly selected sale, define the following events:

17. Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), “E” or “e” (used in scientific notation). Complex numbers should be in the form (a + bi) where “a” and “b” need to have explicitly stated values. For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not.

18. Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), “E” or “e” (used in scientific notation). Complex numbers should be in the form (a + bi) where “a” and “b” need to have explicitly stated values. For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not. math 302 midterm exam.

Suppose that the average weekly earnings for employees in general automotive repair shops is $450, and that the standard deviation for the weekly earnings for such employees is $50. A sample of 100 such employees is select at random.

19. Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), “E” or “e” (used in scientific notation). Complex numbers should be in the form (a + bi) where “a” and “b” need to have explicitly stated values.

For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not. math 302 midterm exam

20. Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), “E” or “e” (used in scientific notation). Complex numbers should be in the form (a + bi) where “a” and “b” need to have explicitly stated values.

For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not.

21. Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), “E” or “e” (used in scientific notation). Complex numbers should be in the form (a + bi) where “a” and “b” need to have explicitly stated values. For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not.

22. Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), “E” or “e” (used in scientific notation). Complex numbers should be in the form (a + bi) where “a” and “b” need to have explicitly stated values. For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not.

The mean weight of loads of coal placed in train cars by a loading machine is 43.0 tons with a standard deviation of 8.0 tons. Assuming that the weight of loads placed in the train cars by this loader are normally distribut, if a random sample of 9 loads is chosen for a weight check, find the probability that the mean weight of those loads is more than 40.60 tons.

23. Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), “E” or “e” (used in scientific notation). Complex numbers should be in the form (a + bi) where “a” and “b” need to have explicitly stated values.

For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not. math 302 midterm exam

**PART 9 OF 9**

24. Using the standard normal curve, the Z- score representing the 85th percentile is 0.67

25. The sampling distribution of the mean will have the same mean as the original population from which the samples were drawn.

## [Solved] MATH 302 MIDTERM EXAM 2 – QUESTION AND ANSWERS|AMERICAN PUBLIC UNIVERSITY

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