# MATHEMATICS

Question 15 of 25 1.0 Points

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). NOTE: For scientific notation, a period MUST be used as the decimal point marker.

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 annual returns, in percentages, on stocks A and B for three possible states of the economy are given in the table below.

Economy State Probability StockA StockB

Good 0.5 40 20

Average 0.3 20 40

Bad 0.2 10 8

If one invested in StockA, what would be the expected annual percentage return? Place your answer, in percent, in the blank. For example, an expected 10 percent return would be recorded as 10. Do not use a percent sign.

Part 7 of 9 –

Question 16 of 25 1.0 Points

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). NOTE: For scientific notation, a period MUST be used as the decimal point marker.

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.

If a coin is tossed seven times, how many different outcomes are possible? Place your answer in the blank. Do not use any decimal places or commas. For example, 345 would be a legitimate entry.

Question 17 of 25 1.0 Points

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). NOTE: For scientific notation, a period MUST be used as the decimal point marker.

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 Big Triple at the local racetrack consists of picking the correct order of finish of the first three horses in the ninth race. If there are 12 horses entered in today’s ninth race, how many Big Triple outcomes are possible? Place your answer, as a whole number—no decimal places—in the blank. For example 667 would be a legitimate entry.

Part 8 of 9 –

Question 18 of 25 1.0 Points

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.

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 selected at random.

Find the standard deviation of the sampling distribution of the means of average weekly earnings for samples of size 100. Place your answer in the blank. Do not include a dollar sign. For example, 7 would be a legitimate entry.

Question 19 of 25 1.0 Points

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.

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 selected at random.

Find the probability that the mean of the sample is greater than $460. Place your answer, rounded to 4 decimal places, in the blank. For example, 0.2345 would be a legitimate answer.

Question 20 of 25 1.0 Points

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 average hourly wage of workers at a fast food restaurant is $6.50/hr with a standard deviation of $0.45. Assume that the distribution is normally distributed. If a worker at this fast food restaurant is selected at random, what is the probability that the worker earns more than $6.75? Place your answer, rounded to 4 decimal places, in the blank. For example, 0.1776 would be a legitimate entry.

Question 21 of 25 1.0 Points

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.

A popular retail store knows that the purchase amounts by its customers is a random variable that follows a normal distribution with a mean of $30 and a standard deviation of $9.

What are the two dollar amounts, equidistant from the mean of $30, such that 90% of all customer purchases are between these values? Place your answers in the blanks provided. Do not include a dollar sign. For example, 14.25 would be a legitimate entry.

Lower value

Upper value

Question 22 of 25 1.0 Points

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.

A set of final exam scores in an organic chemistry course was found to be normally distributed, with a mean of 73 and a standard deviation of 8.

What is the probability of getting a score of 68 or less on this exam? Place your answer, rounded to 4 decimal places in the blank. For example, 0.3456 would be a legitimate entry.

Question 23 of 25 1.0 Points

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.

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 selected at random.

Find the mean of the sampling distribution of the means of average weekly earnings for samples of size 100. Place your answer in the blank. Do not include a dollar sign. For example, 123 would be a legitimate entry.

Part 9 of 9 –

Question 24 of 25 1.0 Points

Using the standard normal curve, the Z- score representing the 75th percentile is approximately 0.674. True

False

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Question 25 of 25 1.0 Points

If Z is a standard normal variable, then P(Z = 1) = 0.3413. True

False