QUMT Ch5-6

A town recently dismissed 9 employees in order to meet their new budget reductions. The town had 7 employees over 50 years of age and 17 under 50. If the dismissed employees were selected at random, what is the probability that exactly 7 employees were over 5050? Express your answer as a fraction or a decimal number rounded to four decimal places.

.0001

The number of weaving errors in a twenty-foot by ten-foot roll of carpet has a mean of 0.6. What is the probability of observing no more than 3 errors in the carpet? Round your answer to four decimal places.

.0034 poisson method

You are ordering a hamburger and can get up to 8 toppings, but each topping can only be used once. You tell the cashier to surprise you with the toppings you get. What is the probability that you get 0 toppings? Express your answer as a fraction or a decimal number rounded to four decimal places.

.0039

Parents have always wondered about the sex of a child before it is born. Suppose that the probability of having a male child was 0.5, and that the sex of one child is independent of the sex of other children. What is the probability of having no more than 3 boys out of 8 children? Round your answer to four decimal places.

.3633**

Out of 450 applicants for a job, 211 are female and 53 are female and have a graduate degree. Step 2 of 2: If 97 of the applicants have graduate degrees, what is the probability that a randomly chosen applicant is female, given that the applicant has a graduate degree? Express your answer as a fraction or a decimal rounded to four decimal places.

.5464

A newspaper company classifies its customers by gender and location of residence. The research department has gathered data from a random sample of 1769 customers. The data is summarized in the table below.

.6603**

A newspaper company classifies its customers by gender and location of residence. The research department has gathered data from a random sample of 1802 customers. The data is summarized in the table below. What is the probability that a customer is not female or does not live with their parents? Express your answer as a fraction or a decimal number rounded to four decimal places.

.9567 number of females living with parents given = 78 1-(78/1802)= .9567

A card is drawn from a standard deck of 52 playing cards. What is the probability that the card will be a heart and not a seven? Express your answer as a fraction or a decimal number rounded to four decimal places

12/52=.2308

A card is drawn from a standard deck of 52 playing cards. What is the probability that the card will be a diamond or a jack? Express your answer as a fraction or a decimal number rounded to four decimal places.

13+4-1 (subtract jack of diamonds)/52= .3077

A card is drawn from a standard deck of 52 playing cards. What is the probability that the card will be a spade and not an ace? Express your answer as a fraction or a decimal number rounded to four decimal places.

13/52-1/52=12/52=.2308

How many ways can Nick choose 5 pizza toppings from a menu of 13 toppings if each topping can only be chosen once?

13C5 =1287

A coin is tossed 8 times. What is the probability of getting at least one tail? Express your answer as a fraction or a decimal number rounded to four decimal places.

Binomial trials= 8 p= .5 x= 0 p-(X=x) ans= .9961

The Magazine Mass Marketing Company has received 18 entries in its latest sweepstakes. They know that the probability of receiving a magazine subscription order with an entry form is 0.5. What is the probability that no more than 5 of the entry forms will include an order? Round your answer to four decimal places.

Binomial: x= 0,1,2,3,4,5 .0481

A small liberal arts college in the Northeast has 350 freshmen. Seventy of the freshmen are education majors. Suppose fifty freshmen are randomly selected (without replacement). Step 1 of 2 : Find the expected number of education majors in the sample. Round your answer to two decimal places, if necessary.

Expected Value: n(k/N) n=50 k=70 N=350 Ans= 10

A bank has to repossess 100 homes. Eighty-four of the repossessed homes have market values that are less than the outstanding balance of the mortgage. An auditor randomly selects 25 of the repossessed homes (without replacement) and records the number of homes that have market values less than the outstanding balance of the mortgage. Step 2 of 2 : Find the standard deviation of the number of homes the auditor will find with market values less than the outstanding balance of the mortgage. Round your answer to four decimal places, if necessary.

Find Variance: n(k/N)(1-k/N)*(N-n)/N-1) n=25 N=100 k=84 variance= 2.54545 SD= 1.5954

Write out the sample space for the given experiment. Use the letter H to indicate heads and T for tails. 3 coins are tossed.

HHH,HHT,HTH,HTT,THH,THT,TTH,TTT

Determine whether the following events are mutually exclusive. Choosing a red card or a spade out of a standard deck of cards.

Mutually Exclusive

Determine whether the following events are mutually exclusive. Choosing a heart or a spade out of a standard deck of cards.

Mutually exclusive

There are 6 black balls and 7 red balls in an urn. If 4 balls are drawn without replacement, what is the probability that less than 3 black balls are drawn? Express your answer as a fraction or a decimal number rounded to four decimal places.

N=13 n=4 k=6 x=3,4 Find P(X=x)= 1-[p(X=3)+p(X=4)] ans: .7833

Which plan has the least amount of risk? Plan a: $0=.21 $45,000=.53 $90,000=.26 Plan B: -$10,000=.26 $35,000=.33 $75,000=.41

Plan a has the least risk

Write out the sample space for the given experiment. Use the letter R to indicate red, G to indicate green, and B to indicate blue. A die shows 3 different colors on it. Give the sample space for the next 2 rolls.

RR,RG,RB,BR,BG,BB,GR,GG,GB (3^2=9, so you should have nine sample spaces in the end)

Decide if the following probability is classical, relative frequency, or subjective. You calculate that the probability of randomly choosing a student who is right-handed is about 44%.

Relative Frequency Probability

Decide if the following probability is classical, relative frequency, or subjective. You believe that you have an 8% chance of getting into an accident on your way to the mall

Subjective Probability

A fair die will be rolled 12 times. What is the probability that 4, 5, or 6 is rolled less than 6 but more than 3 times? Round your answer to four decimal places.

binomial trials = 12 p= .5 x= 4,5 ans= .3142

A company produces optical-fiber cable with a mean of 0.6 flaws per 100 feet. What is the probability that there will be more than 3 flaws in 100 feet of cable? Round your answer to four decimal places.

h= 6.6 x=0,1,2,3 1-p(X=x) ans = .8949

The number of weaving errors in a twenty-foot by ten-foot roll of carpet has a mean of 0.6. What is the probability of observing no more than 2 errors in the carpet? Round your answer to four decimal places.

h=.6 x= 0, 1, 2 ans= .9769

Which plan has the least risk? plan a -15k=.15 20k=.22 70k=.63 plan b -45k=.17 20k=.61 40k=.22

plan b

A pharmacist receives a shipment of 21 bottles of a drug and has 5 of the bottles tested. If 5 of the 21 bottles are contaminated, what is the probability that at least 4 of the tested bottles are contaminated? Express your answer as a fraction or a decimal number rounded to four decimal places.

x=4,5 n=5 k=5 N=21 ans= .0040

There are 217 plastic chips numbered 1 through 217 in a box. What is the probability of reaching into the box and randomly drawing the chip numbered 168? Express your answer as a simplified fraction or a decimal rounded to four decimal places.

.0046

There are 75 students in a chemistry class. The instructor must choose two students at random. What is the probability that a junior Chemistry major (15) and then a senior Chemistry (2) major are chosen at random? Express your answer as a fraction or a decimal number rounded to four decimal places.

.0054

At a hospital, patients arrive at a rate of 66 patients per hour. What is the average number of patients that would arrive in a 10 minute period?

11

Suppose a batch of 70 light bulbs contains 7 light bulbs that are defective. Let X be the number of defective light bulbs in a random sample of 20 light bulbs (where the sample is taken without replacement). Step 1 of 2 : Find the expected number of defective bulbs. Round your answer to two decimal places, if necessary.

2

Suppose you like to keep a jar of change on your desk. Currently, the jar contains the following: 30- Pennies 19- Nickels 22-Dimes 24- Quarters What is the probability that you reach into the jar and randomly grab a dime and then, without replacement, a nickel? Express your answer as a fraction or a decimal number rounded to four decimal places.

22/95 * 19/94= .0468

A 22-sided die is rolled 4 times. How many different outcomes are possible?

22^4= 234256

A card is drawn from a standard deck of 52 playing cards. What is the probability that the card will be a spade or a face card? Express your answer as a fraction or a decimal number rounded to four decimal places.

3/52=.0577

A doctor visits her patients during morning rounds. In how many ways can the doctor visit 88 patients during the morning rounds?

40320

A 2424-sided die is rolled 55 times. How many different outcomes are possible?

7962624

Parents have always wondered about the sex of a child before it is born. Suppose that the probability of having a male child was 0.5, and that the sex of one child is independent of the sex of other children. What is the probability of having at least 2 girls out of 4 children? Round your answer to four decimal places.

Binomial: Trials: 4 p= .5 x= 0,1 1-p(X=x) =.6875

A bank has to repossess 100 homes. Eighty-four of the repossessed homes have market values that are less than the outstanding balance of the mortgage. An auditor randomly selects 25 of the repossessed homes (without replacement) and records the number of homes that have market values less than the outstanding balance of the mortgage. Step 1 of 2 : Find the expected number of homes the auditor will find with market values less than the outstanding balance of the mortgage. Round your answer to the nearest whole number, if necessary.

Formula of Expected Value: n(k/N) n=25 k= 84 N= 100 ans=21

A town recently dismissed 10 employees in order to meet their new budget reductions. The town had 5 employees over 50 years of age and 19 under 50. If the dismissed employees were selected at random, what is the probability that exactly 1 employee was over 50? Express your answer as a fraction or a decimal number rounded to four decimal places.

K=5 N=24 n=10 x=1 ans= .2355

The auto parts department of an automotive dealership sends out a mean of 3 special orders daily. What is the probability that, for any day, the number of special orders sent out will be more than 5? Round your answer to four decimal places.

h= 3 x= 0,1,2,3,4,5 1-p(X=x) ans: .0839

A company produces optical-fiber cable with a mean of 0.5 flaws per 100 feet. What is the probability that there will be more than 3 flaws in 1200 feet of cable? Round your answer to four decimal places.

h= 6 x= 0, 1, 2, 3 1-p(X=x) Poisson*** ans= .8488

The number of weaving errors in a twenty-foot by ten-foot roll of carpet has a mean of 0.6. What is the probability of observing at least 3 errors in the carpet? Round your answer to four decimal places.

h=.6 x=0, 1, 2 1-p(X=x) =.0231

The number of weaving errors in a twenty-foot by ten-foot roll of carpet has a mean of 0.7. What is the probability of observing at least 3 errors in the carpet? Round your answer to four decimal places.

h=.7 x= 0, 1, 2 1-p(X=x) =.0341

The computer that controls a bank's automatic teller machine crashes a mean of 0.3 times per day. What is the probability that, in any seven-day week, the computer will crash more than 3 times? Round your answer to four decimal places.

h=2.1 (.3*7) x=0,1,2,3 ans: .1614

A bank has to repossess 100 homes. Fifty-four of the repossessed homes have market values that are less than the outstanding balance of the mortgage. An auditor randomly selects 5 of the repossessed homes (without replacement) and records the number of homes that have market values less than the outstanding balance of the mortgage. Step 2 of 2 : What is the probability that none of the audited homes will have outstanding balances in excess of the mortgage? Round your answer to four decimal places, if necessary.

x=5 n= 5 k= 54 N=100 ANS= .0420

A well-mixed cookie dough will produce cookies with a mean of 7 chocolate chips apiece. What is the probability of getting a cookie with less than 2 chips? Round your answer to four decimal places.

.0073

A card is drawn from a standard deck of 5252 playing cards. What is the probability that the card will be a heart and a seven? Express your answer as a fraction or a decimal number rounded to four decimal places.

.0192

Suppose that on the average, 8 students enrolled in a small liberal arts college have their automobiles stolen during the semester. What is the probability that exactly 3 students will have their automobiles stolen during the current semester? Round your answer to four decimal places.

.0286

A well-mixed cookie dough will produce cookies with a mean of 6 chocolate chips apiece. What is the probability of getting a cookie with more than 5 chips? Round your answer to four decimal places.

.5543**

How many ways can Nick choose 2 pizza toppings from a menu of 7 toppings if each topping can only be chosen once?

21 7C2

A standard six-sided die is rolled 19 times. What is the expected value of the number of times a 1, 2, or 3 will be rolled? Do not round your answer.

3/6 n=19 19*.5= 9.5

Out of 450 applicants for a job, 211 are female and 53 are female and have a graduate degree. Step 1 of 2: What is the probability that a randomly chosen applicant has a graduate degree, given that they are female? Express your answer as a fraction or a decimal rounded to four decimal places.

53/211=.2512

You are ordering a new home theater system that consists of a TV, surround sound system, and DVD player. You can choose from 6 different TVs, 12 types of surround sound systems, and 18 types of DVD players. How many different home theater systems can you build?

6*12*18= 1296

Out of 450 applicants for a job, 238 are female and 69 are female and have a graduate degree. Step 2 of 2: If 110 of the applicants have graduate degrees, what is the probability that a randomly chosen applicant is female, given that the applicant has a graduate degree? Express your answer as a fraction or a decimal rounded to four decimal places.

69/110=.6273

Which probability is based on educated guesses

Subjective probability

Parents have always wondered about the sex of a child before it is born. Suppose that the probability of having a male child was 0.5, and that the sex of one child is independent of the sex of other children. What is the probability of having more than 2 girls out of 10 children? Round your answer to four decimal places.

binomial n=10 p=.5 x=0,1,2 1-p(X=x) ans=.9453**

The auto parts department of an automotive dealership sends out a mean of 4.4 special orders daily. What is the probability that, for any day, the number of special orders sent out will be less than 3? Round your answer to four decimal places.

h=4.4 x=0,1,2 =.1851

Events are mutually exclusive when...

they cannot occur at the same time

The Magazine Mass Marketing Company has received 10 entries in its latest sweepstakes. They know that the probability of receiving a magazine subscription order with an entry form is 0.5. What is the probability that more than two-fifths of the entry forms will include an order? Round your answer to four decimal places.

trials: 10 p: .5 x: more than 4 (2/5) ans: .623

Which plan has the least amount of risk? Plan a: -10000=.61 25000=.15 55000=.24 plan b: -15000=.16 -10000=.43 30000=.41

variance of plan a= : σ2=∑[xi2⋅P(X=xi)]−μ2=763,027,500 SQRT/SD= 27622.95 variance of plan B: σ2=∑[xi2⋅P(X=xi)]−μ2=416,640,000 SQRT/SD = 20411.76

Suppose a batch of 100 light bulbs contains 4 light bulbs that are defective. Let X be the number of defective light bulbs in a random sample of 30 light bulbs (where the sample is taken without replacement). Step 1 of 2 : Find the probability that at most 3 of the bulbs sampled will be defective. Round your answer to four decimal places, if necessary.

x= 3 n= 30 k= 4 N= 100 ans: .9930

Naval intelligence reports that 8 enemy vessels in a fleet of 17 are carrying nuclear weapons. If 6 vessels are randomly targeted and destroyed, what is the probability that at least 5 vessels transporting nuclear weapons were destroyed? Express your answer as a fraction or a decimal number rounded to four decimal places.

x=5,6 n=6 k=8 N=17 P(X=5)=8C5⋅(17-8)C(6−5)/17C6=504/12376 P(X=6)=8C6⋅(17-8)C(6−6)/17C6=28/12376 504/12376 + 28/12376 = 532/12376 =.0430 ANS= .0430

A company produces optical-fiber cable with a mean of 0.40.4 flaws per 100100 feet. What is the probability that there will be less than 22 flaws in 11001100 feet of cable? Round your answer to four decimal places

.0668**

The auto parts department of an automotive dealership sends out a mean of 5.2 special orders daily. What is the probability that, for any day, the number of special orders sent out will be less than 3? Round your answer to four decimal places.

.1088

The auto parts department of an automotive dealership sends out a mean of 7.3 special orders daily. What is the probability that, for any day, the number of special orders sent out will be exactly 5? Round your answer to four decimal places.

.116703

What is the probability of rolling a sum of 6 on a standard pair of six-sided dice? Express your answer as a fraction or a decimal number rounded to three decimal places, if necessary.

.1389

The auto parts department of an automotive dealership sends out a mean of 3.1 special orders daily. What is the probability that, for any day, the number of special orders sent out will be exactly 4? Round your answer to four decimal places.

.1733**

The auto parts department of an automotive dealership sends out a mean of 4.3 special orders daily. What is the probability that, for any day, the number of special orders sent out will be exactly 3? Round your answer to four decimal places.

.1798**

A card is drawn from a standard deck of 52 playing cards. What is the probability that the card will be a spade and not a club? Express your answer as a fraction or a decimal number rounded to four decimal places.

.25

A card is drawn from a standard deck of 52 playing cards. What is the probability that the card will be a diamond and not a club? Express your answer as a fraction or a decimal number rounded to four decimal places.

.2500

A coin is tossed 6 times. What is the probability of getting at least one tail? Express your answer as a fraction or a decimal number rounded to four decimal places.

.9843 binomial dist trials=6 n=.5 x=0 1-p(X=x)

Out of 450 applicants for a job, 238 are female and 69 are female and have a graduate degree. Step 1 of 2: What is the probability that a randomly chosen applicant has a graduate degree, given that they are female? Express your answer as a fraction or a decimal rounded to four decimal places.

69/238=.2899

A quality control inspector has drawn a sample of 14 light bulbs from a recent production lot. Suppose that 50% of the bulbs in the lot are defective. What is the expected value of the number of defective bulbs in the sample? Do not round your answer.

7

How many ways can Marie choose 2 pizza toppings from a menu of 8 toppings if each topping can only be chosen once?

8!/(8-2)!2!= 28

A newspaper company classifies its customers by gender and location of residence. The research department has gathered data from a random sample of 1383 customers. The data is summarized in the table below. What is the probability that a customer is not female (793) or does not live with their parents (1254)? Express your answer as a fraction or a decimal number rounded to four decimal places.

Find the number of females that live with their parents (given) =55 Now find the probability the customer is a female that lives with her parents. 55/1383 Now find the compliment of that event: 1-(55/1383)=

Lost-time accidents occur in a company at a mean rate of 0.7 per day. What is the probability that the number of lost-time accidents occurring over a period of 10 days will be no more than 2? Round your answer to four decimal places

h= .7*10=7 x=2,1,0 ans: .0296

The number of weaving errors in a twenty-foot by ten-foot roll of carpet has a mean of 0.7. What is the probability of observing less than 4 errors in the carpet?

x= Number of weaving errors Mean=.7 Find the probability that less than four errors occur. P(x=0)+p(x=1)+p(x=2)+p(x=3)=.9942

A town recently dismissed 7 employees in order to meet their new budget reductions. The town had 4 employees over 50 years of age and 16 under 50. If the dismissed employees were selected at random, what is the probability that more than 1 employee was over 50? Express your answer as a fraction or a decimal number rounded to four decimal places.

x=0,1 n=7 k=4 N=20 Find P(X=x)= 1-[p(X=0)+p(X=1)] ans: .4392

A coin is tossed 7 times. What is the probability of getting at least one tail? Express your answer as a fraction or a decimal number rounded to four decimal places.

.9922

A coin is tossed 9 times. What is the probability of getting at least one tail? Express your answer as a fraction or a decimal number rounded to four decimal places.

.9980

A coin is tossed 10 times. What is the probability of getting at least one tail? Express your answer as a fraction or a decimal number rounded to four decimal places.

.9990 Binomial trials = 10 p= .5 x=0 1-p(x=x) ans=.9990

The number of weaving errors in a twenty-foot by ten-foot roll of carpet has a mean of 0.7. What is the probability of observing less than 5 errors in the carpet? Round your answer to four decimal places.

.9992

Find the standard deviation of the following data. Round your answer to one decimal place. X= -8, P(X=x)=.02 (follow same pattern) -7,.2 -6,.1 -5,.1 -4,.1 -3,.3

Find variance 1st: -5.4 33 33-(-5.4)^2=3.84 sqrt of 3.84=1.959

A quality control inspector has drawn a sample of 18 light bulbs from a recent production lot. Suppose 20% of the bulbs in the lot are defective. What is the probability that exactly 5 bulbs from the sample are defective? Round your answer to four decimal places.

N= 18 P=.2 X=5 formula = nCx*p^x*(1-p)^(n-x) 18C5*.2^18*(1-.2)^(18-5) =.1507

The auto parts department of an automotive dealership sends out a mean of 5.9 special orders daily. What is the probability that, for any day, the number of special orders sent out will be more than 4? Round your answer to four decimal places.

Poisson: h= 5.9 x= 0,1,2,3,4 1-p(X=x) ans= .7013

A quality control inspector has drawn a sample of 14 light bulbs from a recent production lot. Suppose 20% of the bulbs in the lot are defective. What is the probability that exactly 4 bulbs from the sample are defective? Round your answer to four decimal places.

Use binomial probability: n=14 p=.2 x=4 (.20 C 4) * 0.20^4 * (0.80)^10: .1720

An aluminum foil manufacturer wants to improve the quality of his product and is trying to develop a probability model for the flaws that occur in a sheet of foil. Assume that X, the number of flaws per square foot, has a Poisson distribution. If flaws occur randomly at an average of one flaw per 40 square feet, what is the probability that a box containing a 80 square foot roll will contain more than one flaw? Round your answer to four decimal places, if necessary.

h=2 1-[P(x=0)+P(x=1)]=? 1-(.13534+.27067)= .5940

An aluminum foil manufacturer wants to improve the quality of his product and is trying to develop a probability model for the flaws that occur in a sheet of foil. Assume that X, the number of flaws per square foot, has a Poisson distribution. If flaws occur randomly at an average of one flaw per 85 square feet, what is the probability that a box containing a 425 square foot roll will contain more than one flaw?

h=425/85=5 x=0,1 ans=.9596

A company produces optical-fiber cable with a mean of 0.6 flaws per 100 feet. What is the probability that there will be exactly 3 flaws in 1300 feet of cable? Round your answer to four decimal places.

h=7.8 (1300/100=13. 13*.6=7.8) x=3 ans=.0324

A company produces optical-fiber cable with a mean of 0.7 flaws per 100 feet. What is the probability that there will be more than 4 flaws in 1400 feet of cable? Round your answer to four decimal places.

h=9.8 x= 0, 1, 2, 3, 4 1-p(X=x) ans= .9667

A pharmacist receives a shipment of 17 bottles of a drug and has 4 of the bottles tested. If 5 of the 17 bottles are contaminated, what is the probability that exactly 2 of the tested bottles are contaminated? Express your answer as a fraction or a decimal number rounded to four decimal places.

k=5 N=17 n=4 x=2 ANS= .2773

A small liberal arts college in the Northeast has 350 freshmen. Seventy of the freshmen are education majors. Suppose fifty freshmen are randomly selected (without replacement). Step 2 of 2 : Find the standard deviation of the number of education majors in the sample. Round your answer to two decimal places, if necessary.

n(k/N)(1-k/N)*(N-n)/N-1) abs: 2.6224

You are ordering a hamburger and can get up to 6 toppings, but each topping can only be used once. You tell the cashier to surprise you with the toppings you get. What is the probability that you get 2 toppings? Express your answer as a fraction or a decimal number rounded to four decimal places.

nCx*p^x*(1-p)^(n-x) n=6 x= 2 p= .5 ans= .2344

You are ordering a hamburger and can get up to 8 toppings, but each topping can only be used once. You tell the cashier to surprise you with the toppings you get. What is the probability that you get 2 toppings? Express your answer as a fraction or a decimal number rounded to four decimal places.

nCx*p^x*(1-p)^(n-x) n=8 x= 2 p= .5 ans= .1094

A mail order company classifies its customers by gender and location of residence. The research department has gathered data from a random sample of 1532 customers. The data is summarized in the table below. What is the probability that a customer is not female or does not live with their parents? Express your answer as a fraction or a decimal number rounded to four decimal places.

number of females living with parents given = 209 1-(209/1532) = .8636

Which plan has the least amount of risk? plan a: 25000=.65 60000=.21 75000=.14 plan b -5000=.63 0=.25 55000=.12

plan b; payout * p -5000*.63 and so on. total = 3450 now, payout^2*p -5000^2*.63 total = 378750000 now to find the variance for plan b: 378,750,000-(3450)^2 =366,847,500 now find the standard deviation: SQRT of variance = 19153.26 The standard deviation for plan a= 20033.16 plan b would be the least risky

Suppose a batch of 70 light bulbs contains 7 light bulbs that are defective. Let X be the number of defective light bulbs in a random sample of 20 light bulbs (where the sample is taken without replacement). Step 2 of 2 : Find the probability that at least 1 of the bulbs sampled will be defective. Round your answer to four decimal places, if necessary.

x= 0 n= 20 k=7 N=70 Use compliment rule ans: .9167

Suppose a batch of 50 light bulbs contains 5 light bulbs that are defective. Let X be the number of defective light bulbs in a random sample of 20 light bulbs (where the sample is taken without replacement). Step 2 of 2 : Find the probability that at least 1 of the bulbs sampled will be defective. Round your answer to four decimal places, if necessary.

x= 0 n=20 k= 5 N= 50 Use the compliment rule: Ans: .9327

Unknown to a medical researcher, 7 out of 20 patients have a heart problem that will result in death if they receive the test drug. 5 patients are randomly selected to receive the drug and the rest receive a placebo. What is the probability that at least 4 patients will die? Express your answer as a fraction or a decimal number rounded to four decimal places.

x= 4,5 n= 5 k=7 N=20 ans: .0307

A bank has to repossess 100 homes. Forty-seven of the repossessed homes have market values that are less than the outstanding balance of the mortgage. An auditor randomly selects 5 of the repossessed homes (without replacement) and records the number of homes that have market values less than the outstanding balance of the mortgage. Step 1 of 2 : What is the probability that all of the audited homes will have outstanding balances in excess of the mortgage? Round your answer to four decimal places, if necessary.

x=0 n= 5 k= 47 N= 100 ans:.0381

A pharmacist receives a shipment of 22 bottles of a drug and has 4 of the bottles tested. If 4 of the 22 bottles are contaminated, what is the probability that none of the tested bottles are contaminated? Express your answer as a fraction or a decimal number rounded to four decimal places.

x=0 n=4 k=4 N=22 ans= .4183

A bank has to repossess 100 homes. Fifty-four of the repossessed homes have market values that are less than the outstanding balance of the mortgage. An auditor randomly selects 5 of the repossessed homes (without replacement) and records the number of homes that have market values less than the outstanding balance of the mortgage. Step 1 of 2 : What is the probability that all of the audited homes will have outstanding balances in excess of the mortgage? Round your answer to four decimal places, if necessary.

x=0 n=5 k=54 N=100 ans: .0182

The number of calls received by an office on Monday morning between 8:00 AM and 9:00 AM has a mean of 7. Calculate the probability of getting exactly 3 calls between eight and nine in the morning. Round your answer to four decimal places.

x=3 Mean=7 =.0521

Suppose a batch of 100 light bulbs contains 4 light bulbs that are defective. Let X be the number of defective light bulbs in a random sample of 30 light bulbs (where the sample is taken without replacement). Find the probability that more than 4 of the bulbs sampled will be defective. Round your answer to four decimal places, if necessary.

x=3,4 n=30 k=4 N=100 Trick question: 0

Naval intelligence reports that 7 enemy vessels in a fleet of 16 are carrying nuclear weapons. If 5 vessels are randomly targeted and destroyed, what is the probability that less than 4 vessels transporting nuclear weapons were destroyed? Express your answer as a fraction or a decimal number rounded to four decimal places.

x=4,5 n=5 k=7 N=16 ans: .9231

A town recently dismissed 9 employees in order to meet their new budget reductions. The town had 7 employees over 50 years of age and 17 under 50. If the dismissed employees were selected at random, what is the probability that exactly 5 employees were over 50? Express your answer as a fraction or a decimal number rounded to four decimal places.

x=5 n=9 k=7 N=24 ans= .0382