# Probability and Statistics Final Exam Review SHORT

## Transcription

Probability and Statistics Final Exam Review SHORT

Probability and Statistics Final Exam Review SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response. 1) A single six-sided die is rolled. Find the probability of rolling a number less than 3. 1) 2) A study of 1000 randomly selected flights of a major airline showed that 782 of the flights arrived on time. What is the probability of a flight arriving on time? 2) 3) If one card is drawn from a standard deck of 52 playing cards, what is the probability of drawing an ace? 3) 4) In a survey of college students, 880 said that they have cheated on an exam and 1721 said that they have not. If one college student is selected at random, find the probability that the student has cheated on an exam. 4) 5) The distribution of blood types for 100 Americans is listed in the table. If one donor is selected at random, find the probability of selecting a person with blood type A+ or A-. 5) Blood Type O+ Number 37 O6 A+ 34 A6 B+ 10 B2 AB+ 4 AB1 6) The distribution of Master's degrees conferred by a university is listed in the table. 6) Major Frequency Mathematics 216 English 207 Engineering 75 Business 176 Education 222 What is the probability that a randomly selected student graduating with a Master's degree has a major of Engineering? Round your answer to three decimal places. 7) Classify the statement as an example of classical probability, empirical probability, or subjective probability. The probability that it will rain tomorrow is 24%. 7) 8) Classify the statement as an example of classical probability, empirical probability, or subjective probability. The probability that a train will be in an accident on a specific route is 1%. 8) 9) Classify the events as dependent or independent. Event A: A red candy is selected from a package with 30 colored candies and eaten. Event B: A blue candy is selected from the same package and eaten. 9) 1 10) Classify the events as dependent or independent. The events of getting two aces when two cards are drawn from a deck of playing cards and the first card is not replaced before the second card is drawn. 10) 11) A group of students were asked if they carry a credit card. The responses are listed in the table. 11) Class Freshman Sophomore Total Credit Card Not a Credit Card Carrier Carrier Total 46 14 60 32 8 40 78 22 100 If a student is selected at random, find the probability that he or she is a freshman given that the student owns a credit card. Round your answers to three decimal places. 12) A group of students were asked if they carry a credit card. The responses are listed in the table. Class Freshman Sophomore Total 12) Credit Card Not a Credit Card Carrier Carrier Total 14 46 60 17 23 40 31 69 100 If a student is selected at random, find the probability that he or she is a sophomore and owns a credit card. Round your answers to three decimal places. 13) Find the probability of answering the two multiple choice questions correctly if random guesses are made. Assume the questions each have five choices for the answer. Only one of the choices is correct. 13) 14) A multiple-choice test has five questions, each with five choices for the answer. Only one of the choices is correct. You randomly guess the answer to each question. What is the probability that you answer the first two questions correctly? 14) 15) You are dealt two cards successively without replacement from a standard deck of 52 playing cards. Find the probability that the first card is a two and the second card is a ten. Round your answer to three decimal places. 15) 16) Decide if the events A and B are mutually exclusive or not mutually exclusive, A die is rolled. A: The result is a 3. B: The result is an odd number. 16) 17) Decide if the events A and B are mutually exclusive or not mutually exclusive. A card is drawn from a standard deck of 52 playing cards. A: The result is a club. B: The result is a king. 17) 2 18) A card is drawn from a standard deck of 52 playing cards. Find the probability that the card is an ace or a king. 18) 19) The events A and B are mutually exclusive. If P(A) = 0.2 and P(B) = 0.4, what is P(A or B)? 19) 20) Determine the probability distribution's missing value. The probability that a tutor will see 0, 1, 2, 3, or 4 students 20) x 0 1 2 3 4 P(x) 0.01 0.04 0.37 0.34 ? 21) State whether the variable is discrete or continuous. The speed of a car on a Los Angeles freeway during rush hour traffic 21) 22) The random variable x represents the number of cars per household in a town of 1000 households. Find the probability of randomly selecting a household that has at least one car. 22) Cars Households 0 125 1 428 2 256 3 108 4 83 23) A sales firm receives an average of four calls per hour on its toll-free number. For any given hour, find the probability that it will receive exactly nine calls. Use the Poisson distribution. 23) 24) A company ships computer components in boxes that contain 30 items. Assume that the probability of a defective computer component is 0.2. Use the geometric variance to find the variance of defective parts. 24) 25) A car towing service company averages two calls per hour. Use the Poisson distribution to determine the probability that in a randomly selected hour the number of calls is three. 25) 26) Assume that male and female births are equally likely and that the birth of any child does not affect the probability of the gender of any other children. Find the probability of at most three boys in ten births. 26) 27) State whether the variable is discrete or continuous. The blood pressures of a group of students the day before their final exam 27) 28) The probability that an individual is left-handed is 0.11. In a class of 40 students, what is the probability of finding five left-handers? 28) 29) A test consists of 10 multiple choice questions, each with five possible answers, one of which is correct. To pass the test a student must get 60% or better on the test. If a student randomly guesses, what is the probability that the student will pass the test? 29) 3 30) Basketball player Chauncey Billups of the Detroit Pistons makes free throw shots 88% of the time. Find the probability that he misses his first shot and makes the second. 30) 31) A statistics professor finds that when he schedules an office hour at the 10:30 a.m. time slot, an average of three students arrives. Use the Poisson distribution to find the probability that in a randomly selected office hour no students will arrive. 31) 32) A test consists of 330 true or false questions. If the student guesses on each question, what is the mean number of correct answers? 32) 33) Sixty-five percent of men consider themselves knowledgeable football fans. If 12 men are randomly selected, find the probability that exactly two of them will consider themselves knowledgeable fans. 33) 34) In a pizza takeout restaurant, the following probability distribution was obtained. The random variable x represents the number of toppings for a large pizza. Find the mean and standard deviation. 34) x 0 1 2 3 4 P(x) 0.30 0.40 0.20 0.06 0.04 35) At a raffle, 10,000 tickets are sold at $5 each for three prizes valued at $4,800, $1,200, and $400. What is the expected value of one ticket? 35) 36) State whether the variable is discrete or continuous. The number of phone calls to the attendance office of a high school on any given school day 36) 37) The probability that an individual is left-handed is 0.15. In a class of 70 students, what is the mean and standard deviation of the number of left-handers in the class? 37) 38) In a raffle, 1,000 tickets are sold for $2 each. One ticket will be randomly selected and the winner will receive a laptop computer valued at $1200. What is the expected value for a person that buys one ticket? 38) Decide which probability distribution -binomial, geometric, or Poisson- applies to the question. You do not need to answer the question. 39) Given: The probability that a federal income tax return is filled out incorrectly with an 39) error in favor of the taxpayer is 20%. Question: What is the probability that of the ten tax returns randomly selected for an audit in a given week, three returns will contain only errors favoring the taxpayer? 40) Given: The probability that a federal income tax return is filled out incorrectly with an error in favor of the taxpayer is 20%. Question: What is the probability that of the ten tax returns randomly selected for an audit, three returns will contain only errors favoring the taxpayer? 4 40) 41) Given: The probability that a federal income tax return is filled out incorrectly with an error in favor of the taxpayer is 20%. Question: What is the probability that when the ten tax returns are randomly selected for an audit, the sixth return will contain only errors favoring the taxpayer? 5 41)