MATH-11-SP18: Module 2 Quiz

The mean amount of time it takes a kidney stone to pass is 14 days and the standard deviation is 6 days. Suppose that one individual is randomly chosen. Let X=time to pass the kidney stone. Round all answers to two decimal places. A. X ~ N( , ) B. Find the probability that a randomly selected person with a kidney stone will take longer than 21 days to pass it. C. Find the minimum number for the upper quarter of the time to pass a kidney stone. days.

14 6 .12 1805

Americans receive an average of 17 Christmas cards each year. Suppose the number of Christmas cards is normally distributed with a standard deviation of 6. Let X be the number of Christmas cards received by a randomly selected American. Round all answers to two decimal places. A. X ~ N( , ) B. If an American is randomly chosen, find the probability that this American will receive no more than 11 Christmas cards this year. C. If an American is randomly chosen, find the probability that this American will receive between 10 and 20 Christmas cards this year. D. 63% of all Americans receive at most how many Christmas cards?

17 6 .16 .57 19l

The patient recovery time from a particular surgical procedure is normally distributed with a mean of 4.2 days and a standard deviation of 1.7 days. Let X be the recovery time for a randomly selected patient. Round all answers to two decimal places. A. X ~ N( , ) B. What is the median recovery time? days. C. What is the Z-score for a patient that took 2 days to recover? D. What is the probability of spending more than 6 days in recovery? E. What is the probability of spending between 4 and 5 days in recovery? days. F. The 80th percentile for recovery times is? days.

4.2 1.7 4.2 -1.29 .14 .23 5.63

The age of the children in kindergarten on the first day of school is uniformly distributed between 4.8 and 5.8 years old. A first time kindergarten child is selected at random. Round all answers to two decimal places. A. The mean of the distribution is B. The standard deviation is C. The probability that the child will be older than 5 years old is D. The probability that the child will be between 5.2 and 5.7 years old is E. If such a child is at the 45th percentile, how old is that child? years old.

5.3 .3 .8 .5 5.25

The average American man consumes 9.8 grams of sodium each day. Suppose that the sodium consumption of American men is normally distributed with a standard deviation of 0.9 grams. Suppose an American man is randomly chosen. Le X = the amount of sodium consumed. Round all numeric answers to 2 decimal places. A. X ~ N( , ) B. Find the probability that this American man consumes between 9 and 10 grams of sodium per day. C. The middle 20% of American men consume between what two weights of sodium? Low: High:

9.8 .9 .4 9.57 10.03

The student council is hosting a drawing to raise money for scholarships. They are selling tickets for $5 each and will sell 800 tickets. There is one $2,000 grand prize, three $300 second prizes, and fifteen $20 third prizes. You just bought a ticket. Find the expected value for your profit.

-1.0 (with margin: 0.02)

Complete the following probability distribution function table. x P(x) -4 [response1] 0 0.14 5 0.32 20 0.41

.13 <p>The probabilities add to 1.</p> <p>1 - 0.14 - 0.32 - 0.41 = 0.13</p>

Complete the following probability distribution function table. x P(x) 1 0.3 3 [response1] 7 0.2 12 0.4

0.1 (with margin: 0.01)

Complete the following probability distribution function table. x P(x) -4 0.31 -2 0.14 0 0.07 2 [response1] 4 0.28

0.2 (with margin: 0.01)

If a distribution is normal, then it is not possible to randomly select a value that is more than 4 standard deviations from the mean.

False

If the profit on a raffle ticket has an expected value of -5 dollars, then the most likely outcome of purchasing a raffle ticket is a net loss of $5.

False

If two six sided dice are rolled, then the sum of the dice is an example of a continuous random variable.

False

If x is a random variable with a general normal distribution and if a is a positive number and if P(x > a) = 0.24, then P(x < -a) is also 0.24.

False

If x represents a random variable coming from a normal distribution and P(x > 15.7) = 0.04, then P(x < -15.7) = 0.04.

False

If the expected value for a five dollar raffle ticket is 0.85, then there is a 85% chance that the ticket will win.

False, we can only say that if many raffle tickets are purchased then the average return is likely to be $0.85. Notice that this is a dollar amount, not a probability.

Describe what is meant by a binomial (or Bernoulli) distribution.

The distribution of the result of an experiment with -A fixed number of trials -The trials are independent -Each trial results in success or failure -The probability of success, p, is the same for each trial.

Answer the following True or False: For a binomial experiment with 20 trials P(r < 4) = P(r > 16).

False

For a binomial experiment with 20 trials P(r < 4) = P(r > 16).

False

15 cards are selected out of a 52 card deck such that after each card is selected, it is placed back into the deck and the deck is reshuffled. Then the total number of hearts selected follows a binomial distribution.

True

200 randomly selected Americans are asked if they smoke cigarettes. Then the results of this procedure can be treated as a binomial distribution.

True

A survey is taken of 35 randomly selected LTCC students asking them, "Do you plan to transfer to a university next year?" The distribution of possible responses of the 35 students is an example of a binomial distribution.

True

Answer the following questions and round your answers to 2 decimal places. 66% of Americans are home owners. If 45 Americans are selected at random, find the probability that A. Exactly 30 of them are home owners. B. At most 25 of them are are home owners. C. More than 33 of them are are home owners. D. Between 27 and 32 (including 27 and 32) of them are are home owners.

.12. .09 .11. .65

Answer the following questions and round your answers to 2 decimal places. 75% of owned dogs in the United States are spayed or neutered. If 47 dogs are randomly selected, find the probability that A. Exactly 36 of them have been spayed or neutered. B. At most 30 of them have been spayed or neutered. C. At least 35 of them have been spayed or neutered. D. Between 30 and 40 (including 30 and 40) of them have been spayed or neutered.

.13. .06 .61. .94

Answer the following questions and round your answers to 2 decimal places. 31% of all college students major in STEM (Science, Technology, Engineering, and Math). If 36 students are randomly selected, find the probability that A. Exactly 11 of them major in STEM. B. Fewer than 10 of them major in STEM. C. More than 13 of them major in STEM. D. Between 10 and 15 (including 10 and 15) of them major in STEM.

.14. .28 .20. .66

Answer the following questions and round your answers to 2 decimal places. 84% of all Americans live in cities with population greater than 50,000 people. If 50 Americans are selected at random, find the probability that A. Exactly 42 of them live in cities with population greater than 50,000 people. B. At most 45 of them live in cities with population greater than 50,000 people. C. More than 40 of them live in cities with population greater than 50,000 people. D. Between 35 and 40 (including 35 and 40) of them live in cities with population greater than 50,000 people.

.15. .92 .73. .27

Answer the following questions and round your answers to 2 decimal places. 13% of all Americans live in poverty. If 45 Americans are randomly selected, find the probability that A. Exactly 5 of them live in poverty. B. At most 5 of them live in poverty. C. At least 5 of them live in poverty. D. Between 3 and 6 (including 3 and 6) of them live in poverty.

.17. .46 .71. .58

Answer the following questions and round your answers to 2 decimal places. 70% of bald eagles survive their first year of life. If 25 bald eagles are selected at random, find the probability that A. Exactly 18 of them survive their first year of life. B. At most 19 of them survive their first year of life. C. More than 16 of them survive their first year of life. D. Between 15 and 22 (including 15 and 22) of them survive their first year of life.

.17. .81 .68. .89

Suppose that the duration of a particular type of criminal trial is known to be normally distributed with a mean of 18 days and a standard deviation of 5 days. Let X be the number of days for a randomly selected trial. Round all answers to two decimal places. A. X ~ N( , ) B. If one of the trials is randomly chosen, find the probability that it lasted at least 21 days. C. If one of the trials is randomly chosen, find the probability that it lasted between 15 and 20 days. D. 85% of all of these types of trials are completed within how many days?

18 5 .27 .38 23

The round off error when measuring the distance that a long jumper has jumped is uniformly distributed between 0 and 5 mm. Round all answers to two decimal places. A. The mean of this distribution is B. The standard deviation is C. The probability that the round off error for a jumper's distance is exactly 2.5 mm is P(x = 2.5) = D. The probability that the round off error for the distance that a long jumper has jumped is between 2 and 4 mm is P(2 < x < 4) = E. The probability that the jump's round off error is greater than 1 is P(x > 1) = F. P(x > 4 | x > 2) = G. Find the 60th percentile. H. Find the minimum for the upper quartile.

2.5 1.44 0 .4 .8 .33 3 3.75

Suppose that you are offered the following "deal". You roll a die. If you roll a 1, you win $20. If you roll a 2 or 3, you win $5. If you roll a 4, 5, or 6, you pay $15. A. Complete the PDF Table. List the x values from largest to smallest. x P(x) _ _ _ _ _ _ B. Find the expected value. C. Interpret the expected value. D. Based on the expected value, should you play this game?

20. .17 5. .33 -15. .5 -2.45 If you play many games you will likely win on average about this much. No, since the expected value is negative, you would be very likely to come home with less money if you played many games.

The amount of calories consumed by customers at the Chinese buffet is normally distributed with mean 2885 and standard deviation 651. One randomly selected customer is observed to see how many calories X that customer consumes. Round all answers to two decimal places. A. X ~ N( , ) B. Find the probability that the customer consumes less than 2000 calories. C. What proportion of the customers consume over 5,000 calories? D. The Piggy award will given out to the 1% of customers who consume the most calories. What is the least amount of calories a person must consume to receive the Piggy award?

2885 651 .09 0 4399

Los Angeles workers have an average commute of 29 minutes. Suppose the LA commute time is normally distributed with a standard deviation of 13 minutes. Let X represent the commute time for a randomly selected LA worker. Round all answers to two decimal places. A. X ~ N( , ) B. Find the probability that a randomly selected LA worker has a commute that is longer than 40 minutes. C.Find the 90th percentile for the commute time of LA workers.

29 13 .2 46

Suppose that the weight of an newborn fawn is uniformly distributed between 2 and 4 kg. Suppose that a newborn fawn is randomly selected. Round all answers to two decimal places. A. The mean of this distribution is B. The standard deviation is C. The probability that the fawn will weigh more than 2.8 kg. D. Suppose that it is known that the fawn weighs less than 3.5 kg. Find the probability that the fawn weights more than 3 kg.= E. Find the 90th percentile for the weight of fawns.

3 .58 .6 .33 3.8

In China, 4-year-olds average 3 hours a day unsupervised. Most of the unsupervised children live in rural areas, considered safe. Suppose that the standard deviation is 1.5 hours and the amount of time spent alone is normally distributed. We randomly survey one Chinese 4-year-old living in a rural area. We are interested in the amount of time X the child spends alone per day. (Source: San Jose Mercury News) Round all answers to two decimal places. A. X ~ N( , ) B. Find the probability that the child spends less than 2 hours per day unsupervised. C. What percent of the children spend over 12 hours per day unsupervised? percent. D. 60 percent of all children spend at least how many hours per day unsupervised? hours.

3 1.5 .25 0 2.6

The percent of fat calories that a person in America consumes each day is normally distributed with a mean of about 36 and a standard deviation of 10. Suppose that one individual is randomly chosen. Let X=percent of fat calories. Round all answers to two decimal places. A. X ~ N( , ) B. Find the probability that a randomly selected fat calorie percent is more than 28. C. Find the minimum number for the upper quarter of percent of fat calories.

36 10 .79 42.74

A survey is taken of 90 randomly selected Americans asking them, "Do you think congress should vote to change the constitution?" The distribution of possible responses of the 90 Americans is an example of a binomial distribution.

True

Exactly 50% of the area under the normal curve lies to the right of the mean.

True

Given a survey conducted of randomly selected people, the number of siblings people have is a discrete random variable and the distance from their bellybuttons to their knees is a continuous random variable.

True

The time that it takes for the next train to come follows a distribution with f(x) = 0.05 where x goes between 15 and 35 minutes. Round all numerical answers to two decimal places. A. This is a distribution. B. It is a distribution. C. The mean of this distribution is D. The standard deviation is E. Find the probability that the time will be at most 30 minutes. F. Find the probability that the time will be between 25 and 30 minutes = G. Find the 80th percentile.

uniform continuous 25 5.77 .75 .25 31

The student council is hosting a drawing to raise money for scholarships. They are selling tickets for $1 each and will sell 3000 tickets. There is one $500 grand prize, four $100 second prizes, and thirty $10 third prizes. You just bought a ticket. Find the expected value for your profit.

-0.6 (with margin: 0.02)

Suppose that you are offered the following "deal." You roll a die. If you roll a 6, you win $10. If you roll a 4 or 5, you win $5. If you roll a 1, 2, or 3, you pay $8. A. Complete the PDF Table. List the x values from largest to smallest. x P(x) _ _ _ _ _ _ B. Find the expected value. 0.23 C. Interpret the expected value. [ Select ] D. Based on the expected value, should you play this game?

10. .17 5. .33 -8. .5 -.65. If you play many games you will likely win on average very close to this amount. No, since the expected value is negative, you would be very likely to come home with less money if you played many games.

IQ is normally distributed with a mean of 100 and a standard deviation of 15. Suppose one individual is randomly chosen. Let X=IQ of an individual. Round all answers to two decimal places. A. X ~ N( , ) B. Find the probability that a randomly selected person's IQ is over 105. C. A school offers special services for all children in the bottom 3% for IQ scores. What is the highest IQ score a child can have and still receive special services? D. Find the Inter Quartile Range (IQR) for IQ scores. Q1: Q3: IQR:

100 15 .37 71.8 90 110 20

The mean height of an adult giraffe is 18 feet. Suppose that the distribution is normally distributed with standard deviation 0.8 feet. Let X be the height of a randomly selected adult giraffe. Round all answers to two decimal places. A. X ~ N( , ) B. What is the median giraffe height? ft. C. What is the Z-score for a 20 foot giraffe? D. What is the probability that a randomly selected giraffe will be shorter than 17 feet tall? E. What is the probability that a randomly selected giraffe will be between 16 and 19 feet tall? F. The 90th percentile for the height of giraffes is ft.

18 ,8 18 2.5 .11 .89 19.03

In the 1992 presidential election, Alaska's 40 election districts averaged 1956.8 votes per district for President Clinton. The standard deviation was 572.3. (There are only 40 election districts in Alaska.) The distribution of the votes per district for President Clinton was bell-shaped. Let X= number of votes for President Clinton for an election district. (Source: The World Almanac and Book of Facts) Round all answers to two decimal places. A. X ~ N( , ) B. Is 1956.8 a population mean or a sample mean? C. Find the probability that a randomly selected district had fewer than 1700 votes for President Clinton. D. Find the probability that a randomly selected district had between 2000 and 2700 votes for President Clinton. E. Find the first quartile for votes for President Clinton.

1957 572 Population mean .33 .37 1571

Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed with a mean of 246 feet and a standard deviation of 39 feet. Let X be the distance in feet for a fly ball. Round all answers to two decimal places. A. X ~ N( , ) B. Find the probability that a randomly hit fly ball travels less than 200 feet. C.Find the 70th percentile for the distribution of fly balls.

246 39 .12 266

The number of ants per acre in the forest is normally distributed with mean 45,289 and standard deviation 12,340. Let X= number of ants in a randomly selected acre of the forest. Round all answers to two decimal places. A. X ~ N( , ) B. Find the probability that a randomly acre in the forest has fewer than 40,000 ants. C. Find the probability that a randomly selected acre has between 35,000 and 50,000 ants. D. Find the first quartile.

45289 12340 .33 .45 36966

The average number of words in a romance novel is 64,182 and the standard deviation is 17,154. Assume the distribution is normal. Let X be the number of words in a randomly selected romance novel. Round all answers to two decimal places. A. X ~ N( , ) B. Find the proportion of all novels that are between 50,000 and 60,000 words. C. The 90th percentile for novels is words. D. The middle 40% of romance novels have from words to

64182 17154 .2 86166 55186 73178

Suppose that the speed at which cars go on the freeway is normally distributed with mean 68 mph and standard deviation 5 miles per hour. Let X be the speed for a randomly selected car. Round all answers to two decimal places. A. X ~ N( , ) B. If one car is randomly chosen, find the probability that is traveling more than 70 mph. C. If one of the cars is randomly chosen, find the probability that it is traveling between 65 and 75 mph. D. 90% of all cars travel at least how fast on the freeway? mph.

68 5 .34 .65 61.59

Since the area under the normal curve within two standard deviations of the mean is 0.95, the area under the normal curve that corresponds to values greater than 2 standard deviations above the mean is 0.05.

False

Ten cards are selected out of a 52 card deck without replacement and the number of Jacks is observed. This is an example of a Binomial Experiment.

False

A venture capitalist, willing to invest $1,000,000, has three investments to choose from. The first investment, a software company, has a 20% chance of returning $5,000,000 profit, a 30% chance of returning $1,000,000 profit, and a 50% chance of losing the million dollars. The second company, a hardware company, has a 10% chance of returning $3,000,000 profit, a 30% chance of returning $1,000,000 profit, and a 60% chance of losing the million dollars. The third company, a biotech firm, has a 10% chance of returning $6,000,000 profit, a 80% of no profit or loss, and a 10% chance of losing the million dollars. Order the expected values from smallest to largest.

Hardware, Biotech, Software Software Company: 5,000,000 x 0.2 + 1,000,000 x 0.3 + -1,000,000 x 0.5 = 800,000 Hardware Company: 3,000,000 x 0.1 + 1,000,000 x 0.3 + -1,000,000 x 0.6 = 0 Biotech Firm: 6,000,000 x 0.1 + 0 x 0.8 + -1,000,000 x 0.1 = 500,000

If x represents a random variable coming from a normal distribution with mean 3 and if P(x > 4.8) = 0.15, then P(3 < x < 4.8) = 0.35.

True

A venture capitalist, willing to invest $1,000,000, has three investments to choose from. The first investment, a software company, has a 10% chance of returning $5,000,000 profit, a 30% chance of returning $1,000,000 profit, and a 60% chance of losing the million dollars. The second company, a hardware company, has a 20% chance of returning $3,000,000 profit, a 40% chance of returning $1,000,000 profit, and a 40% chance of losing the million dollars. The third company, a biotech firm, has a 10% chance of returning $6,000,000 profit, a 70% of no profit or loss, and a 20% chance of losing the million dollars. Order the expected values from smallest to largest.

Software, Biotech, Hardware Software Company: 5,000,000 x 0.1 + 1,000,000 x 0.3 + -1,000,000 x 0.6 = 200,000 Hardware Company: 3,000,000 x 0.2 + 1,000,000 x 0.4 + -1,000,000 x 0.4 = 600,000 Biotech Firm: 6,000,000 x 0.1 + 0 x 0.7 + -1,000,000 x 0.2 = 400,000

If z is a random variable with a standard normal distribution and if a is a positive number and if P(z > a) = 0.15, then P(-a < z < a) = 0.7.

True

If Z is a random variable from a standard normal distribution and if P(Z<a)=0.42, then P(Z<-a)=0.58.

True

If a business owner, who is only interested in the bottom line, computes the expected value for the profit made in bidding on a project to be -3,000, then this owner should not bid on this project.

True

If a distribution is normal with mean 8 and standard deviation 2, then the median is also 8.

True

If x represents a random variable coming from a normal distribution and P(x < 10.4) = 0.78, then P(x > 10.4) = 0.22.

True