apu math 302 midterm assignment

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Question 1 of 25

0.0/ 1.0 Points

For a boxplot, the vertical line inside the box indicates the location of the

A.median

B.mode

In C.mean

D.inter quartile range

Answer Key:

Part 2 of 9 – 2.0/ 2.0 Points

Question 2 of 25

1.0/ 1.0 Points

If events A and B are mutually exclusive, then the probability of both events occurring simultaneously is equal to

A.0.5

B.1.0

C.any value between 0.5 and 1.0

D.0.0

Answer Key:

Question 3 of 25

1.0/ 1.0 Points

If P(A) = P(A|B), then events A and B are said to be

A.complementary

B.mutually exclusive

C.exhaustive

D.independent

Answer Key:

Part 3 of 9 – 3.0/ 3.0 Points

Question 4 of 25

1.0/ 1.0 Points

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.

What is the probability that greater than 40 batteries will last at least 8 hours?

A.0.0789

B.0.4538

C.0.9598

D.0.0402

Answer Key:

Question 5 of 25

1.0/ 1.0 Points

If a gambler rolls two dice and gets a sum of 10, he wins $10, and if he gets a sum of three, he wins $20. The cost to play the game is $5. What is the expectation of this game?

A.$3.06

B.-$2.78

C.-$3.06

D.$2.78

Answer Key:

Question 6 of 25

1.0/ 1.0 Points

There are two types of random variables, they are

A.real and unreal

B.exhaustive and mutually exclusive

C.complementary and cumulative

D.discrete and continuous

Answer Key:

Part 4 of 9 – 5.0/ 6.0 Points

Question 7 of 25

1.0/ 1.0 Points

The theorem that states that the sampling distribution of the sample mean is approximately normal when the sample size n is reasonably large is known as the:

A.simple random sample theorem

B.central tendency theorem

C.point estimate theorem

D.central limit theorem

Answer Key:

Question 8 of 25

1.0/ 1.0 Points

The normal distribution is:

A.a binomial distribution with only one parameter

B.a discrete distribution

C.a density function of a discrete random variable

D.the single most important distribution in statistics

Answer Key:

Question 9 of 25

1.0/ 1.0 Points

If Z is a standard normal random variable, then the value z for which P(-z < Z < z) equals 0.8764 is A.1.16 B.0.3764 C.1.54 D.3.08 Answer Key: Question 10 of 25 1.0/ 1.0 Points Given that Z is a standard normal random variable, P(-1.0 < Z < 1.5) is A.0.9332 B.0.0919 C.0.7745 D.0.8413 Answer Key: Question 11 of 25 0.0/ 1.0 Points One reason for standardizing random variables is to measure variables with: A.different means and standard deviations on a non-standard scale B.dissimilar means and similar standard deviations in like terms In C.similar means and standard deviations on two scales D.different means and standard deviations on a single scale Answer Key: Question 12 of 25 1.0/ 1.0 Points The standard deviation of a probability distribution is a: A.measure of variability of the distribution B.measure of central location C.measure of skewness of the distribution D.measure of relative likelihood Answer Key: Part 5 of 9 - 1.0/ 1.0 Points Question 13 of 25 1.0/ 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. A sample of 150 students at a State University was taken after the final business statistics exam to ask them whether they went partying the weekend before the final or spent the weekend studying, and whether they did well or poorly on the final. The following table contains the result. Did Well on Exam Did Poorly on Exam Studying for Exam 60 15 Went Partying 22 53 If the sample is a good representation of the population, what percentage of the students in the population should we expect to spend the weekend studying and do poorly on the final exam? Place your answer in the blank, rounded to 2 decimal places. Do not use a percentage sign (%). For example, 44.44 would be a legitimate answer. 10.00 Answer Key: Part 6 of 9 - 2.0/ 2.0 Points Question 14 of 25 1.0/ 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. Find the mean of the distribution shown below. X 0 1 2 P(X) 0.24 0.31 0.45 Round your answer to two decimal place as necessary. For example, 4.56 would be a legitimate entry. Mean = 1.21 Answer Key: Feedback: Expected value = (0)(0.24) + (1)(0.31) + (2)(0.45) = 1.21 Question 15 of 25 1.0/ 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. Find the mean of the following probability distribution. X 1 2 3 4 5 P(X) 0.20 0.10 0.35 0.05 0.30 Round your answer to two decimal place as necessary. For example, 4.56 would be a legitimate entry. Mean = 3.15 Answer Key: Part 7 of 9 - 2.0/ 2.0 Points Question 16 of 25 1.0/ 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. At a certain college, there were 600 science majors, 200 engineering majors, and 500 business majors. If a student is selected at random, what is the probability that the student is an engineering major? Place your answer, rounded to four decimal places, in the blank. 0.1538 When entering your answer do not use any labels or symbols other than a decimal point. Simply provide the numerical value. For example, 0.1234 would be a legitimate entry. Answer Key: 0 Question 17 of 25 1.0/ 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. A reading list for a course contains 20 articles. How many ways are there to choose three articles from this list? Place your answer in the blank. Do not use any decimal places or commas. For example, 45 would be a legitimate entry. 1140 Answer Key: Part 8 of 9 - 5.0/ 6.0 Points Question 18 of 25 1.0/ 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. 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 between $445 and $455. Place your answer, rounded to 4 decimal places, in the blank. For example, 0.2345 would be a legitimate entry. 0.6826 Answer Key: 0. Question 19 of 25 1.0/ 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 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 distributed, 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. Place your answer, rounded to four decimal places, in the blank. 0.8159 When entering your answer do not use any labels or symbols other than a decimal point. Simply provide the numerical value. For example, 0.1234 would be a legitimate entry. Answer Key: 0 Question 20 of 25 1.0/ 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. Scores on a mathematics examination appear to follow a normal distribution with mean of 65 and standard deviation of 15. The instructor wishes to give a grade of “C” to students scoring between the 60th and 70th percentiles on the exam. What score represents the 60th percentile score on the mathematics exam? Place your answer in the blank, rounded to a whole number. For example, 62 would be a legitimate entry. 69 Answer Key: Question 21 of 25 1.0/ 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. A Wendy’s fast-food restaurant sells hamburgers and chicken sandwiches. On a typical weekday, the demand for hamburgers is normally distributed with a mean of 450 and standard deviation of 80 and the demand for chicken sandwiches is normally distributed with a mean of 120 and standard deviation of 30. How many hamburgers must the restaurant stock to be 99% sure of not running out on a given day? Place you answer, rounded to the nearest whole number in the blank. For example, 345 would be a legitimate entry. 637 Answer Key: Question 22 of 25 0.0/ 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 manufacturer of a new compact car claims the miles per gallon (mpg) for the gasoline consumption is mound shaped and symmetric with a mean of 25.9 mpg and a standard deviation of 9.5 mpg. If 30 such cars are tested, what is the probability the average mpg achieved by these 30 cars will be greater than 28? Place your answer, rounded to 4 decimal places, in the blank. 0.3520 Answer Key: 0. Question 23 of 25 1.0/ 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. 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 is the probability that a randomly selected customer will spend less than $15 at this store? Place your answer, rounded to 4 decimal places, in the blank. For example, 0.3456 would be a legitimate entry. .0478 Answer Key: Part 9 of 9 - 1.0/ 2.0 Points Question 24 of 25 1.0/ 1.0 Points The sampling distribution of the mean will have the same mean as the original population from which the samples were drawn. True False Answer Key: True Question 25 of 25 0.0/ 1.0 Points Using the standard normal curve, the Z- score representing the 5th percentile is 1.645. In True False Answer Key:

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