MATH 302 MIDTERM EXAM – QUESTION AND ANSWERS – SET 3 ( LATEST UPDATE )

MATH 302 MIDTERM EXAM – QUESTION AND ANSWERS – SET 3 Part 1 of 9 - 1.0/ 1.0 Points Question 1 of 25 1.0/ 1.0 Points Given the following boxplot where m is the median value, what statement could be made about the distribution of the data? A. The distribution is negatively skewed. B. The distribution is positively skewed. C. The distribution is approximately symmetric. D. No statement can be made about the data because no data values are shown on the plot. Answer Key: C Part 2 of 9 - 2.0/ 2.0 Points Question 2 of 25 1.0/ 1.0 Points The table below shows the preferences for elective courses of students who are undecided about their majors. Philosophy Digital Art Film Studies Male 9 16 22 Female 6 18 14 What is the probability of randomly selecting a student who is female or prefers Digital Art? A.46.2% B.84.7% C.21.2% D.63.5% Answer Key: D Question 3 of 25 1.0/ 1.0 Points The formal way to revise probabilities based on new information is to use: A.unilateral probabilities B.conditional probabilities C.common sense probabilities D.complementary probabilities Answer Key: B Part 3 of 9 - 3.0/ 3.0 Points Question 4 of 25 1.0/ 1.0 Points Find the variance of the following probability distribution. X P(X) 1 0.10 2 0.35 3 0.10 4 0.15 5 0.30 A.1.44 B.2.06 C.1.76 D.1.2 Answer Key: B Question 5 of 25 1.0/ 1.0 Points The following data were obtained from a survey of college students. The variable X represents the number of non- assigned books read during the past six months. x 0 1 2 3 4 5 P (X=x) 0.20 0.25 0.20 0.15 0.10 0.10 What is the expected value of X? A.6.25 B.1.20 C.3.65 D.2.0 Answer Key: D Question 6 of 25 1.0/ 1.0 Points Find the variance of the following probability distribution. X P(X) 1 0.10 2 0.20 3 0.35 4 0.30 5 0.05 A.1.1 B.1.21 C.1.05 D.1.02 Answer Key: A Part 4 of 9 - 6.0/ 6.0 Points Question 7 of 25 1.0/ 1.0 Points One reason for standardizing random variables is to measure variables with: A.similar means and standard deviations on two scales B.dissimilar means and similar standard deviations in like terms C.different means and standard deviations on a single scale D.different means and standard deviations on a non-standard scale Answer Key: C Question 8 of 25 1.0/ 1.0 Points In a normal distribution, changing the standard deviation: A.splits the distribution to two curves B. shifts the curve left or right C. makes the curve more robust D. makes the curve more or less spread out Answer Key: D Question 9 of 25 1.0/ 1.0 Points The continuous distribution characterized by a symmetric, bell-shaped curve is the: A.exponential distribution B. binomial distribution C. normal distribution D. Poisson distribution Answer Key: C Question 10 of 25 1.0/ 1.0 Points The standard deviation of a probability distribution is a: A.measure of skewness of the distribution B. measure of variability of the distribution C. measure of central location D. measure of relative likelihood Answer Key: B Question 11 of 25 1.0/ 1.0 Points The average height of flowering cherry trees in a nursery is 11 feet. If the heights are normally distributed with a standard deviation of 1.6, find the probability that a randomly selected cherry tree in this nursery is less than 13 feet tall. A. 0.67 B.0.89 C.0.95 D.0.11 Answer Key: B Question 12 of 25 1.0/ 1.0 Points The mean of a probability distribution is a: A.measure of variability of the distribution B. measure of relative likelihood C. measure of central location D. measure of skewness of the distribution Answer Key: C 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. Suppose that an analysis of a set of test scores reveals that: . Compute the interquartile range. Place your answer, rounded to 1 decimal place, in the blank. For example, 32.1 would be a legitimate entry. 60.0 Answer Key: 60.0 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. In a history class, students take a weekly multiple choice quiz consisting of 6 questions, each with 4 possible answers. If a student randomly guesses at the answer to each question for every quiz, then what is the mean number of correct answers the student will get on each quiz? Round your answer to one decimal place as necessary. For example, 4.5 would be a legitimate entry. Answer: 1.5 Answer Key: 1.5 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. Ann is applying for a bank loan to open a pizza franchise. She must first complete a written application and then, if the written application is approved, be interviewed by bank officers. If an applicant’s written application is not approved the applicant is not granted an interview with the bank officers. Past records for this bank show that the probability of an applicant having his or her written application approved is 0.63. Records also indicate that the interviewing committee of bank officers approves 85% of the individuals they interview. Find the probability that Ann’s loan request is approved. Place your answer, rounded to 2 decimal places, in the blank. For example, 0.76 would be a legitimate entry. .55 Answer Key: 0.45|0.65 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. Suppose that a marketing firm sends questionnaires to two different companies. Based on historical evidence, the marketing research firm believes that each company, independently of the other, will return the questionnaire with a probability of 0.30. What is the probability that neither of the questionnaires will be returned? Place your answer, rounded to 2 decimal places, in the blank. For example, 0.23 is a legitimate entry. .49 Answer Key: 0.49 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. 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: = chocolate chosen = strawberry chosen = vanilla chosen = ice cream on a cone ice cream in a cup Find the probability that the ice cream was strawberry flavor, given that it was sold on a cone. Place your answer, rounded to 4 decimal places, in the blank. For exampe, 0.3456 would be a legitimate entry. .2915 Answer Key: 0.2915 Part 8 of 9 - 6.0/ 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. 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 91 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. .9675 Answer Key: .9378|1.0000 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. 0.8059 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: 0.7659|0.8659 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. 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 between 65 and 89 on this exam? Place your answer, rounded to 4 decimal places in the blank. For example, 0.3456 would be a legitimate entry. .8185 Answer Key: 0.7686|0.8686 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. 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. .0228 Answer Key: 0.0128|0.0328 Question 22 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 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. Only 5% of the students taking the test scored higher than what value? Place your answer, rounded to a whole number, in the blank. For example, 78 would be a legitimate entry. 85 Answer Key: 83|89 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. It has been observed that electrical connectors manufactured by Jolt Electrical Supply Company last an average of 18.2 months and follow a normal distribution with a standard deviation of 1.7 months. Jolt agrees to replace any connector that fails within 19 months. Out of 500 connectors sold, how many does Jolt expect to replace, on average? Place your answer, rounded to the nearest whole number, in the blank. For example, 123 would be a legitimate answer. 340 Answer Key: 335|345 Part 9 of 9 - 2.0/ 2.0 Points Question 24 of 25 1.0/ 1.0 Points Using the standard normal curve, the Z- score representing the 99th percentile is 2.326. True False Answer Key: True Question 25 of 25 1.0/ 1.0 Points A random variable X is standardized when each value of X has the mean of X subtracted from it, and the difference is divided by the standard deviation of X. True False Answer Key: True