Statistics Exam Practice: Frequency Distribution & Probabilities

Version 1 1 1. The following is a relative frequency distribution of grades in an introductory statistics course. Grade Relative Frequency A 0.22 B ? C 0.18 D 0.17 F 0.06 a. If this was the distribution of 300 students, find the frequency of failures. A) 12 B) 18 C) 30 D) 46 b. What is the probability that a randomly select student get a grade of B or above? 2. Consider the following data on distances traveled by people to visit the local amusement park and calculate the relative frequency for the distances over 16 miles. Distance Frequency 1-8 miles 15 9-16 miles 12 17-24 miles 7 25-32 miles 5 33-40 miles 1 A) .325 B) .150 C) .125 D) .025

Version 1 2 3. At the end of their final exam, 550 students answered an additional question in which they rated their instructor’s teaching effectiveness, with the following results. Student's Rating of Instructor Student's Final Grade Very or Somewhat Effective Very or Somewhat Ineffective A 193 95 B 81 125 C 28 17 D 19 26 F 10 21 a. What proportion of the students who rated their instructor as very or somewhat effective received a B or better in the class A) 0.345 B) 0.254 C) 0.482 D) 0.803 E) 0.828 b. What proportion of the students who rated their instructor as very or somewhat effective received a B or better in the class? A) 0.345 B) 0.254 C) 0.482 D) 0.803 E) 0.828 4. The local amusement park was interested in the average wait time at their most popular roller coaster at the peak park time (2 p.m.). They selected 13 patrons and had them get in line between 2 and 3 p.m. Each was given a stopwatch to record the time they spent in line. The times recorded were as follows (in minutes; mean = 114.15): 118, 124, 108, 116, 99, 120, 148, 118, 119, 121, 45, 130, 118. What is the standard deviation? A) 103 B) 23.62 C) 557.97 D) 128.8 E) 115

Version 1 3 5. Suppose that a company's annual sales were $1,000,000 in 1999. The annual growth rate of sales from 1999 to 2000 was 18 percent, from 2000 to 2001 it was − 10 percent, and from 2001 to 2002 it was 32 percent. a. What is the geometric mean growth rate over this three-year period? A) 0.119 B) 0.133 C) 0.145 D) 0.156 E) 0.160 b. What are the forecasted sales for 2003? A) 1,780,678 B) 1,401,840 C) 1,965,337 D) 1,613,371 6. Employees of a local university have been classified according to gender and job type. Gender Job Male (M) Female (F) Faculty (FA) 120 40 Salaried Staff (SS) 30 60 Hourly Staff (HS) 50 50 If an employee is selected at random, what is the probability that the employee is male? A) .667 B) .367 C) .333 D) .500 E) .571

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Version 1 4 7. At a college, 60 percent of the students are women, and 45 percent of the students receive a grade of C. Twenty-five percent of the students are neither female nor C students. a. Fill out the following contingency table C Not C Total Women 0.60 Men 0.25 Total 0.45 b. What is the probability that a randomly selected student is female and a C student? A) .30 B) .50 C) .70 D) .25 8. A family has two children. What is the probability that both are girls, given that at least one is a girl? A) 1/8 B) 1/4 C) 1/2 D) 1/3 E) 1/6 9. Using the following probability distribution table of the random variable x , what is the probability of x = 3? 𝑋 𝑃(𝑋) 0 5/15 1 4/15 2 1/15 3 A) 3/15 B) 5/15 C) 1/15 D) 2/15

Version 1 5 10. A fair die is rolled 10 times. What is the probability that an odd number (1, 3, or 5) will occur fewer than 3 times? A) .0547 B) .1172 C) .1550 D) .7752 E) .8450 11. A large disaster cleaning company estimates that 30 percent of the jobs it bids on are finished within the bid time. Looking at a random sample of 8 jobs that it has contracted, calculate the probability that exactly 4 of the jobs were not completed within the bid time. A) .0081 B) .8059 C) .0580 D) .1361 12. The random variable x has a uniform distribution when x lies between the values of 4 and 10. What is the probability 𝑃(𝑋 = 10) ? A) 0 B) 1 C) 1/6 D) 1/14 13. A study shows that employees who begin their workday at 9:00 a.m. vary their times of arrival uniformly from 8:40 a.m. to 9:30 a.m. The probability that a randomly chosen employee reports to work between 9:00 and 9:10 is _______. A) 40 percent. B) 20 percent. C) 10 percent. D) 30 percent. E) 16.7 percent. 14. The area under the normal curve between 𝑧 = 0 and 𝑧 = 1 is ________ the area under the normal curve between 𝑧 = 1 and 𝑧 = 2 . A) less than B) greater than C) equal to D) less than, greater than, or equal to, depending on the value of the mean, E) less than, greater than, or equal to, depending on the value of the standard deviation,

Version 1 6 15. If the random variable, 𝑋 , is normally distributed and has a mean of 𝜇 and a standard deviation 𝜎 , then the mean and standard deviation, respectively, of (𝑋 − µ)/𝜎 are A) 𝜇 and 𝜎 . B) 𝑋 and 𝑠 . C) 1 and 0. D) 0 and 1. 16. What is the probability that a standard normal random variable will be between −2 and 2? A) .4772 B) .0228 C) .9772 D) .9544 17. Find 𝑧 when the area to the right of 𝑧 is .1314. A) 𝑧 = 1.12 B) 𝑧 = .55 C) 𝑧 = −.55 D) 𝑧 = −1.12

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BSTAT 5325 Exam 1 practice

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