STT 315 Practice Problems II for Sections

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1 STT 315 Practice Problems II for Sections MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the problem. 1) Classify the following random variable according to whether it is discrete or continuous. The temperature in degrees Fahrenheit on July 4th in Juneau, Alaska A) continuous B) discrete 2) Classify the following random variable according to whether it is discrete or continuous. The number of goals scored in a soccer game A) discrete B) continuous 3) Classify the following random variable according to whether it is discrete or continuous. The number of phone calls to the attendance office of a high school on any given school day A) continuous B) discrete 4) A discrete random variable x can assume five possible values: 2, 3, 5, 8, 10. Its probability distribution is shown below. Find the probability for the value of x = 5. 1) 2) 3) 4) x p(x) ??? A) 0.2 B) 0.3 C) 0.1 D) 0.7 5) The Fresh Oven Bakery knows that the number of pies it can sell varies from day to day. The owner believes that on 50% of the days she sells 100 pies. On another 25% of the days she sells 150 pies, and she sells 200 pies on the remaining 25% of the days. To make sure she has enough product, the owner bakes 200 pies each day at a cost of $2 each. Assume any pies that go unsold are thrown out at the end of the day. If she sells the pies for $5 each, find the probability distribution for her daily profit. A) B) Profit P(profit) Profit P(profit) $300.5 $ $ C) Profit P(profit) $100.5 $ $ $300.5 $ $ D) Profit P(profit) $500.5 $ $ ) Consider the given discrete probability distribution. Find P(x > 3). 5) 6) x p(x) A).7 B).5 C).2 D).3 1

2 7) Consider the given discrete probability distribution. Find P(x 4). 7) x p(x) A).95 B).05 C).10 D).90 8) Mamma Temte bakes six pies each day at a cost of $2 each. On 11% of the days she sells only two pies. On 17% of the days, she sells 4 pies, and on the remaining 72% of the days, she sells all six pies. If Mama Temte sells her pies for $4 each, what is her expected profit for a day's worth of pies? [Assume that any leftover pies are given away.] A) -$8.00 B) -$6.78 C) $20.88 D) $8.88 9) A local bakery has determined a probability distribution for the number of cheesecakes it sells in a given day. The distribution is as follows: 8) 9) Number sold in a day Prob (Number sold) Find the number of cheesecakes that this local bakery expects to sell in a day. A) 14.1 B) 10 C) D) 20 10) Calculate the mean for the discrete probability distribution shown here. 10) X P(X) A) 6.5 B) 8.04 C) 2.01 D) 26 11) A discrete random variable x can assume five possible values: 2, 3, 5, 8, 10. Its probability distribution is shown below. Find the standard deviation of the distribution. 11) x p(x) A) 5.7 B) C) 6.41 D) ) Which binomial probability is represented on the screen below? 12) A) P(x 4) B) P(x > 4) C) P(x < 4) D) P(x = 4) 2

3 13) We believe that 95% of the population of all Business Statistics students consider statistics to be an exciting subject. Suppose we randomly and independently selected 21 students from the population. If the true percentage is really 95%, find the probability of observing 20 or more students who consider statistics to be an exciting subject. Round to six decimal places. A) B) C) D) ) A recent study suggested that 70% of all eligible voters will vote in the next presidential election. Suppose 20 eligible voters were randomly selected from the population of all eligible voters. Use a binomial probability table to find the probability that more than 12 of the eligible voters sampled will vote in the next presidential election. A) B) C) D) E) ) A recent study suggested that 70% of all eligible voters will vote in the next presidential election. Suppose 20 eligible voters were randomly selected from the population of all eligible voters. Use a binomial probability table to find the probability that more than 10 but fewer than 16 of the 20 eligible voters sampled will vote in the next presidential election. A) B) C) D) ) It a recent study of college students indicated that 30% of all college students had at least one tattoo. A small private college decided to randomly and independently sample 15 of their students and ask if they have a tattoo. Use a binomial probability table to find the probability that exactly 5 of the students reported that they did have at least one tattoo. A) B) C) D) ) The probability that an individual is left-handed is In a class of 70 students, what is the mean and standard deviation of the number of left-handed students? Round to the nearest hundredth when necessary. A) mean: 70; standard deviation: 3.02 B) mean: 9.1; standard deviation: 3.02 C) mean: 9.1; standard deviation: 2.81 D) mean: 70; standard deviation: ) The number of traffic accidents that occur on a particular stretch of road during a month follows a Poisson distribution with a mean of 8.8. Find the probability that fewer than three accidents will occur next month on this stretch of road. A) B) C) D) ) The number of traffic accidents that occur on a particular stretch of road during a month follows a Poisson distribution with a mean of 8.9. Find the probability of observing exactly four accidents on this stretch of road next month. A) B) C) D) ) The university police department must write, on average, five tickets per day to keep department revenues at budgeted levels. Suppose the number of tickets written per day follows a Poisson distribution with a mean of 8.9. Find the probability that exactly four tickets are written on a randomly selected day. A) B) C) D) ) The number of goals scored at each game by a certain hockey team follows a Poisson distribution with a mean of 5 goals per game. Find the probability that the team will score more than three goals during a game. A) B) C) D) ) 14) 15) 16) 17) 18) 19) 20) 21) 3

4 22) The number of goals scored at each game by a certain hockey team follows a Poisson distribution with a mean of 5 goals per game. Find the probability that the team scored exactly three goals in each of four randomly selected games. A) B) C) D) ) An alarm company reports that the number of alarms sent to their monitoring center from customers owning their system follow a Poisson distribution with = 4.7 alarms per year. Identify the mean and standard deviation for this distribution. A) mean = 2.17, standard Deviation = 2.17 B) mean = 4.7, standard Deviation = 2.17 C) mean = 2.17, standard Deviation = 4.7 D) mean = 4.7, standard Deviation = ) 23) 24) Given that x is a hypergeometric random variable, compute p(x) for N = 6, n = 3, r = 3, and x = 1. 24) A).125 B).375 C).45 D).55 25) Given that x is a hypergeometric random variable, compute p(x) for N = 8, n = 5, r = 3, and x = 2. 25) A).536 B).343 C).140 D) ) Suppose the candidate pool for two appointed positions includes 6 women and 9 men. All candidates were told that the positions were randomly filled. Find the probability that two men are selected to fill the appointed positions. A).160 B).343 C).360 D) ) Suppose a man has ordered twelve 1-gallon paint cans of a particular color (lilac) from the local paint store in order to paint his mother's house. Unknown to the man, three of these cans contains an incorrect mix of paint. For this weekend's big project, the man randomly selects four of these 1-gallon cans to paint his mother's living room. Let x = the number of the paint cans selected that are defective. Unknown to the man, x follows a hypergeometric distribution. Find the probability that at least one of the four cans selected contains an incorrect mix of paint. A) B) C) D) ) 27) SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 28) You randomly select 7 students from a class with 15 male and 20 female students. What is the probability that you will choose exactly 4 females? 28) MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Answer the question True or False. 29) For a continuous probability distribution, the probability that x is between a and b is the same regardless of whether or not you include the endpoints, a and b, of the interval. A) True B) False 29) Solve the problem. 30) Use the standard normal distribution to find P(-2.25 < z < 1.25). 30) A).8821 B).8944 C).4878 D) ) Use the standard normal distribution to find P(z < or z > 2.33). 31) A).7888 B).9809 C).0606 D)

5 32) Find a value of the standard normal random variable z, called z0, such that P(-z0 z z0) = ) A) 1.96 B) C) 2.33 D).99 33) Find a value of the standard normal random variable z, called z0, such that P(z z0) = ) A) -.47 B) -.53 C) -.81 D) ) For a standard normal random variable, find the probability that z exceeds the value ) A) B) C) D) ) For a standard normal random variable, find the point in the distribution in which 11.9% of the z-values fall below. A) 1.18 B) C) D) ) A physical fitness association is including the mile run in its secondary-school fitness test. The time for this event for boys in secondary school is known to possess a normal distribution with a mean of 450 seconds and a standard deviation of 40 seconds. Find the probability that a randomly selected boy in secondary school can run the mile in less than 358 seconds. A).4893 B).0107 C).5107 D) ) A physical fitness association is including the mile run in its secondary-school fitness test. The time for this event for boys in secondary school is known to possess a normal distribution with a mean of 470 seconds and a standard deviation of 60 seconds. The fitness association wants to recognize the fastest 10% of the boys with certificates of recognition. What time would the boys need to beat in order to earn a certificate of recognition from the fitness association? A) seconds B) seconds C) seconds D) seconds 38) A physical fitness association is including the mile run in its secondary-school fitness test. The time for this event for boys in secondary school is known to possess a normal distribution with a mean of 440 seconds and a standard deviation of 60 seconds. Between what times do we expect approximately 95% of the boys to run the mile? A) between and seconds B) between 0 and seconds C) between and seconds D) between 345 and 535 seconds 39) The volume of soda a dispensing machine pours into a 12-ounce can of soda follows a normal distribution with a mean of ounces and a standard deviation of 0.20 ounce. The company receives complaints from consumers who actually measure the amount of soda in the cans and claim that the volume is less than the advertised 12 ounces. What proportion of the soda cans contain less than the advertised 12 ounces of soda? A).4332 B).5668 C).0668 D) ) The weight of corn chips dispensed into a 48-ounce bag by the dispensing machine has been identified as possessing a normal distribution with a mean of 48.5 ounces and a standard deviation of 0.2 ounce. What proportion of the 48-ounce bags contain more than the advertised 48 ounces of chips? A).4938 B).9938 C).5062 D) ) 36) 37) 38) 39) 40) 5

6 41) The amount of soda a dispensing machine pours into a 12-ounce can of soda follows a normal distribution with a mean of ounces and a standard deviation of 0.20 ounce. Each can holds a maximum of ounces of soda. Every can that has more than ounces of soda poured into it causes a spill and the can must go through a special cleaning process before it can be sold. What is the probability that a randomly selected can will need to go through this process? A).3413 B).6587 C).8413 D) ) Before a new phone system was installed, the amount a company spent on personal calls followed a normal distribution with an average of $900 per month and a standard deviation of $50 per month. Refer to such expenses as PCE's (personal call expenses). Using the distribution above, what is the probability that during a randomly selected month PCE's were between $ and $990.00? A).0001 B).9579 C).0421 D) ) 42) 43) Which of the following statements is not a property of the normal curve? 43) A) P(µ - < x < µ + ).95 B) mound-shaped (or bell shaped) C) symmetric about µ D) P(µ - 3 < x < µ + 3 ) ) Which one of the following suggests that the data set is not approximately normal? 44) A) B) A data set with 68% of the measurements within x ± 2s. C) A data set with IQR = 752 and s = 574. D) Stem Leaves

7 45) Data has been collected and a normal probability plot for one of the variables is shown below. Based on your knowledge of normal probability plots, do you believe the variable in question is normally distributed? The data are represented by the"o" symbols in the plot. 45) A) No. The plot does not reveal a straight line and this indicates the variable is not normally distributed. B) Yes. The plot reveals a curve and this indicates the variable is normally distributed. C) Yes. The plot reveals a straight line and this indicates the variable is normally distributed. Find the probability. 46) Suppose x is a random variable best described by a uniform probability distribution with c = 30 and d = 90. Find P(30 x 60). A) 0.5 B) 0.6 C) 0.3 D) ) Suppose x is a random variable best described by a uniform probability distribution with c = 20 and d = 40. Find P(x < 30). A) 0.6 B) 0.5 C) 0.05 D) ) Suppose x is a random variable best described by a uniform probability distribution with c = 10 and d = 70. Find P(x > 55). A) 0.15 B) C) 0.75 D) ) 47) 48) Solve the problem. 49) A machine is set to pump cleanser into a process at the rate of 7 gallons per minute. Upon inspection, it is learned that the machine actually pumps cleanser at a rate described by the uniform distribution over the interval 6.5 to 9.5 gallons per minute. Find the probability that between 7.0 gallons and 8.0 gallons are pumped during a randomly selected minute. A) 0 B) 1 C) 0.33 D) ) 7

8 50) The diameters of ball bearings produced in a manufacturing process can be described using a uniform distribution over the interval 2.5 to 4.5 millimeters. What is the mean diameter of ball bearings produced in this manufacturing process? A) 3.5 millimeters B) 3.0 millimeters C) 4.5 millimeters D) 4.0 millimeters 50) 51) Suppose x is a uniform random variable with c = 20 and d = 90. Find the standard deviation of x. 51) A) = B) = 3.03 C) = D) = ) The diameters of ball bearings produced in a manufacturing process can be described using a uniform distribution over the interval 8.5 to 10.5 millimeters. Any ball bearing with a diameter of over millimeters or under 8.75 millimeters is considered defective. What is the probability that a randomly selected ball bearing is defective? A) 0 B).25 C).75 D).50 53) A machine is set to pump cleanser into a process at the rate of 10 gallons per minute. Upon inspection, it is learned that the machine actually pumps cleanser at a rate described by the uniform distribution over the interval 9.5 to 12.5 gallons per minute. What is the probability that at the time the machine is checked it is pumping more than 11.0 gallons per minute? A).667 B).7692 C).25 D).50 54) A machine is set to pump cleanser into a process at the rate of 6 gallons per minute. Upon inspection, it is learned that the machine actually pumps cleanser at a rate described by the uniform distribution over the interval 5.5 to 9.5 gallons per minute. Find the variance of the distribution. A) 1.33 B) C) 3.00 D) ) The time between customer arrivals at a furniture store has an approximate exponential distribution with mean = 8.5 minutes. If a customer just arrived, find the probability that the next customer will arrive in the next 5 minutes. A) B) C) D) ) The time between customer arrivals at a furniture store has an approximate exponential distribution with mean = 8.5 minutes. If a customer just arrived, find the probability that the next customer will not arrive for at least 20 minutes. A) B) C) D) ) The time (in years) until the first critical-part failure for a certain car is exponentially distributed with a mean of 3.4 years. Find the probability that the time until the first critical-part failure is 5 years or more. A) B) C) D) ) The time (in years) until the first critical-part failure for a certain car is exponentially distributed with a mean of 3.4 years. Find the probability that the time until the first critical-part failure is less than 1 year. A) B) C) D) ) The time between arrivals at an ATM machine follows an exponential distribution with = 10 minutes. Find the probability that between 15 and 25 minutes will pass between arrivals. A) B) C) D) ) 53) 54) 55) 56) 57) 58) 59) 8

9 Answer the question True or False. 60) The probability density function for an exponential random variable x has a graph called a bell curve. A) True B) False 60) 61) The exponential distribution has the property that its mean equals its standard deviation. 61) A) True B) False Solve the problem. 62) Suppose that the random variable x has an exponential distribution with = 1.5. Find the probability that x will assume a value within the interval µ ± 2. A) B) C) D) ) The time between arrivals at an ATM machine follows an exponential distribution with = 10 minutes. Find the mean and standard deviation of this distribution. A) Mean = 10, Standard Deviation = 3.16 B) Mean = 3.16, Standard Deviation = 3.16 C) Mean = 10, Standard Deviation = 100 D) Mean = 10, Standard Deviation = 10 62) 63) 9

10 Answer Key Testname: PRACTICE ) A 2) A 3) B 4) B 5) C 6) B 7) A 8) D 9) A 10) B 11) B 12) A 13) B 14) C 15) C 16) C 17) C 18) D 19) A 20) D 21) A 22) A 23) B 24) C 25) A 26) B 27) A 28) P(x = 0) = ) B 48) D 49) C 50) A 51) C 52) B 53) D 54) A 55) B 56) B 57) D 58) C 59) A 60) B 61) A 62) D 63) D 29) A 30) A 31) D 32) C 33) B 34) A 35) B 36) B 37) C 38) C 39) C 40) B 41) D 42) B 43) A 44) B 45) A 46) A 10

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