MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Transcription

1 MATH 1342 TEST 3 REVIEW SUMMER 2015 Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the standard deviation of the random variable. 1) The random variable X is the number of houses sold by a realtor in a single month at the Sendsom's Real Estate office. Its probability distribution is given in the table. Round the answer to two decimal places. Houses Sold (x) Probability P(x) ) A) 2.25 B) 4.45 C) 2.62 D) 6.86 Find the indicated binomial probability. Round to five decimal places when necessary. 2) What is the probability that 6 rolls of a fair die will show four exactly 5 times? 2) A) B) C) D) ) A cat has a litter of 7 kittens. Find the probability that exactly 4 of the little furballs are female. Assume that male and female births are equally likely. A) B) C) D) ) Find the indicated probability. Round to four decimal places. 4) In a certain college, 33% of the physics majors belong to ethnic minorities. If 10 students are selected at random from the physics majors, what is the probability that no more than 6 belong to an ethnic minority? A) B) C) D) ) Use a table of areas for the standard normal curve to find the required z-score. 5) Find the z-score for which the area under the standard normal curve to its left is ) A) 1.82 B) C) 1.03 D) 1.75 Use a table of areas to obtain the shaded area under the standard normal curve. 6) 6) A) B) C) D) Use the empirical rule to solve the problem. 7) The systolic blood pressure of 18-year-old women is normally distributed with a mean of 120 mmhg and a standard deviation of 12 mmhg. What percentage of 18-year-old women have a systolic blood pressure between 96 mmhg and 144 mmhg? A) 99.74% B) 95.44% C) 68.26% D) 99.99% 7) 1

2 Use a table of areas for the standard normal curve to find the required z-score. 8) Find the z-score for having area 0.07 to its right under the standard normal curve, that is, find z A) 1.39 B) 1.45 C) 1.48 D) ) Use a table of areas to find the specified area under the standard normal curve. 9) The area that lies between and ) A) B) C) D) ) The area that lies to the right of ) A) B) C) D) Find the standard deviation of the binomial random variable. 11) A die is rolled 20 times and the number of twos that come up is tallied. If this experiment is repeated many times, find the standard deviation for the random variable X, the number of twos. A) B) 2.24 C) D) ) Use a table of areas to find the specified area under the standard normal curve. 12) The area that lies to the left of ) A) B) C) D) Use the empirical rule to solve the problem. 13) The amount of Jen's monthly phone bill is normally distributed with a mean of $73 and a standard deviation of $11. What percentage of her phone bills are between $40 and $106? A) 99.74% B) 95.44% C) 68.26% D) 99.99% 13) Find the requested value. 14) A researcher wishes to estimate the mean resting heart rate for long-distance runners. A random sample of 12 long-distance runners yields the following heart rates, in beats per minute. 14) Use the data to obtain a point estimate of the mean resting heart rate for all long distance runners. A) 67.8 beats per minute B) 64.6 beats per minute C) 66.2 beats per minute D) 69.6 beats per minute Find the requested confidence interval. 15) A college statistics professor has office hours from 9:00 A.M. to 10:30 A.M. daily. A sample of waiting times to see the professor (in minutes) is 10, 12, 20, 15, 17, 10, 30, 28, 35, 28, 19, 27, 25, 22, 33, 37, 14, 21, 20, 23. Assuming = 7.84, find the 95.44% confidence interval for the population mean. A) -7.7 to 7.8 minutes B) 19.5 to 35.1 minutes C) -3.5 to 3.5 minutes D) 18.8 to 25.8 minutes 15) Provide an appropriate response. 16) Find the confidence level that corresponds to a value of of ) A) 5% B) 0.025% C) 95% D) 0.95% 2

3 Find the necessary sample size. 17) Weights of women in one age group are normally distributed with a standard deviation of 10 lb. A researcher wishes to estimate the mean weight of all women in this age group. Find how large a sample must be drawn in order to be 90 percent confident that the sample mean will not differ from the population mean by more than 3.4 lb. A) 25 B) 34 C) 22 D) 24 17) Find the confidence interval specified. 18) 30 people are selected randomly from a certain town. If their mean age is 32.2 and = 8.5, find a 95% confidence interval for the true mean age, µ, of everyone in the town. A) to B) to C) to D) to ) Find the confidence interval specified. Assume that the population is normally distributed. 19) A laboratory tested twelve chicken eggs and found that the mean amount of cholesterol was 207 milligrams with s = 18.1 milligrams. Construct a 95% confidence interval for the true mean cholesterol content of all such eggs. A) to milligrams B) to milligrams C) to milligrams D) to milligrams 20) Thirty randomly selected students took the calculus final. If the sample mean was 92 and the standard deviation was 8.8, construct a 99% confidence interval for the mean score of all students. A) to B) to C) to D) to ) 20) Find the confidence interval specified. 21) A random sample of 93 light bulbs had a mean life of x = 546 hours. Assume that = 26 hours. Construct a 90% confidence interval for the mean life, µ, of all light bulbs of this type. A) to hours B) to hours C) to hours D) to hours 21) Provide an appropriate response. 22) Find the value of that corresponds to a confidence level of 96%. 22) A) 0.04 B) 4 C) 0.96 D) Identify the distribution of the sample mean. In particular, state whether the distribution of x is normal or approximately normal and give its mean and standard deviation. 23) The heights of people in a certain population are normally distributed with a mean of 64 inches and 23) a standard deviation of 3.7 inches. Determine the sampling distribution of the mean for samples of size 40. A) Normal, mean = 64 inches, standard deviation = 0.09 inches B) Normal, mean = 64 inches, standard deviation = 0.59 inches C) Approximately normal, mean = 64 inches, standard deviation = 0.09 inches D) Normal, mean = 64 inches, standard deviation = 3.7 inches For samples of the specified size from the population described, find the mean and standard deviation of the sample mean x. 24) The mean and the standard deviation of the sampled population are, respectively, and n = 49 A) µ = 125.4; = 3.4 B) µ = 24.1; = 3.4 x x x x C) µ x = 201.5; x = 1.3 D) µ x = 3.4; x = ) 3

4 Find the mean of the binomial random variable. Round to two decimal places when necessary. 25) According to a college survey, 22% of all students work full time. Find the mean for the random variable X, the number of students who work full time in samples of size 16. A) 2.75 B) 3.52 C) 4 D) ) 4

5 Answer Key Testname: 1342TEST3REVIEWSUM15 1) C 2) B 3) B 4) B 5) D 6) A 7) B 8) C 9) C 10) B 11) D 12) B 13) A 14) A 15) D 16) C 17) D 18) A 19) D 20) B 21) D 22) A 23) B 24) A 25) B 5