STAT302 WK3 HMWK

0.0521

A coffee shop serves an average of 72 customers per hour during the morning rush. Find the probability that less than 59 customers arrive in an hour during tomorrow's morning rush. Round answer to 4 decimal places. Answer:

0.0379

A coffee shop serves an average of 75 customers per hour during the morning rush. Find the probability that 80 customers arrive in an hour during tomorrow's morning rush. Round answer to 4 decimal places. Answer:

7.5

A coin is flipped 30 times. Find σ². Round to 1 decimal place. Answer:

0.179

A drug is reported to benefit 40% of the patients who take it. If 6 patients take the drug, what is the probability that 4 or more patients will benefit?

8000000

How many different phone numbers are possible in the area code 503, if the first number cannot start with a 0 or 1? Do not use commas in your answer. Answer:

0.0403

If random variable X has a Poisson distribution with mean = 4.5, find the probability that X is more than 8. (That is, find P(X>8) (round to 4 decimal places) Answer:

0.2709

If random variable X has a Poisson distribution with mean = 7, find the probability that X is more than 8. (That is, find P(X>8) (round to 4 decimal places) Answer:

0.9452

If random variable X has a binomial distribution with n =10 and P(success) = p =0.6, find the probability that X is more than 3. (That is, find P(X>3) (round to 4 decimal places) Answer:

0.9936

If random variable X has a binomial distribution with n =10 and P(success) =p =0.2, find the probability that X is less than 6. (That is, find P(X<6) Answer: (round to 4 decimal places)

9

If random variable X has a binomial distribution with n=15 and P(success) =p= 0.6, find the mean of X. That is, find E(X). Round to the whole number. Do not use decimals. Answer:

cannot be determined from the information given

If two events are independent, what is the probability that they both occur?

0.375

In a box there are 3 red cards and 5 blue cards. The cards are well-shuffled. If you pick a card without looking at the box, what is the probability that you pick a red card? (round to 3 decimal places) Answer:

0.026

In the game of roulette, there is a wheel with spaces marked 0 through 36 and a space marked 00. Find the probability of winning if you pick the number 30 and it comes up on the wheel. Round your answer to 3 decimal places. Answer:

Yes, since all the probabilities are between 0 and 1 and the probabilities add up to one

Is the following table a valid discrete probability distribution? X -5, -2.5, 0, 2.5, 5 P(X=x) 0.15, 0.25, 0.32, 0.18, 0.1

4

It is known that 40% of adult workers have a high school diploma. If a random sample of 10 adult workers is selected, what is the expected number of adult workers with a high school diploma? (That is, what is E(X)?) Round to the whole number. Do not use decimals. Answer:

0.1875

It is known that 50% of adult workers have a high school diploma. If a random sample of 5 adult workers is selected, what is the probability that more than 3 of them have a high school diploma? (That is, what is P(X>3) (round to 4 decimal places) Answer:

0.6563

It is known that 50% of adult workers have a high school diploma. If a random sample of 6 adult workers is selected, what is the probability that 3 or more of them have a high school diploma? (That is, find P(X ≤ 3) (round to 4 decimal places) Answer:

0.54

Let X be the number of courses taken by a part-time student at a college. The following table shows the probability distribution of X with probability as a percentage. Number of Courses, x 1, 2, 3 Probability, P(X=x) 46%, 28%, 26%

0.45

Let X be the number of courses taken by a part-time student at a college. The following table shows the probability distribution of X with probability as a percentage. Number of Courses, x 1, 2, 3 Probability, P(X=x) 55%, 28%, 17%

0.54

Let X be the number of courses taken by a part-time student at a college. The following table shows the probability distribution of X with probability as a percentage. What is the probability that a randomly selected part-time student at this college takes at least 2 courses? (That is, find P(X ≥ 2) Number of Courses, X 1, 2, 3 Probability, P(X=x) 46%, 28%, 36%

0.45

Let X be the number of courses taken by a part-time student at a college. The following table shows the probability distribution of X with probability as a percentage. What is the probability that a randomly selected part-time student at this college takes at least 2 courses? (That is, find P(X ≥ 2) Number of Courses, X 1, 2, 3 Probability, P(X=x) 55%, 28%, 17%

0.9021

Suppose a random variable, x, arises from a binomial experiment. If n = 14, and p = 0.13, find the P(X ≤ 3) using Excel. Round answer to 4 decimal places. Answer:

1.2583

Suppose a random variable, x, arises from a binomial experiment. If n = 14, and p = 0.13, find the standard deviation. Round answer to 4 decimal places. Answer:

0.0016

Suppose a random variable, x, arises from a binomial experiment. If n = 25, and p = 0.85, find the P(X = 15) using Excel. Round answer to 4 decimal places. Answer:

175760000

The California license plate has one number followed by three letters followed by three numbers. How many different license plates are possible? Do not use commas in your answer. Answer:

6/38

The casino game, roulette, allows the gambler to bet on the probability of a ball, which spins in the roulette wheel, landing on a particular color, number, or range of numbers. The table used to place bets contains 38 numbers, and each number is assigned to a color and a range. What is the probability of winning when betting on two lines that touch each other on the table as in 1-2-3-4-5-6?

0.8904

The mean number of visitors at a national park in one weekend is 47. Assume the variable follows a Poisson distribution. Find the probability that there will be at most 55 visitors at this park in one weekend. (That is, find P(X ≤ 55)) (round to 4 decimal places) Answer:

0.0375

The mean number of visitors at a national park in one weekend is 52. Assume the variable follows a Poisson distribution. Find the probability that there will be 58 visitors at this park in one weekend. (That is, find P(X=58) (Round answer to 4 decimal places) Answer:

0.1420

The number of M&M's for each color found in a case were recorded in the table below. Blue = 481, Brown = 371, Green = 483, Orange = 544, Red = 372, Yellow = 369 Total = 2620 What is the probability of selecting a red M&M? Round answer to 4 decimal places. Answer:

0.9943

The number of rescue calls received by a rescue squad in a city follows a Poisson distribution with an average of 2.83 rescues every eight hours. What is the probability that the squad will have at most 2 calls in an hour? Round answer to 4 decimal places. Answer:

0.30

The random variable X = the number of vehicles owned. Find the P(X > 2). Round to two decimal places. X 0, 1, 2, 3, 4 P(X=x) 0.1, 0.35, 0.25, 0.2, 0.1

1.55

The random variable X = the number of vehicles owned. Find the expected number of vehicles owned. Round answer to two decimal places. Name of Courses, X 1, 2, 3, 4 Probability, P(X=x) 0.2, 0.35, 0.25, 0.1, 0.1

0.45

The random variable X = the number of vehicles owned. Find the probability that a person owns less than 2 vehicles. Round to two decimal places. X 0, 1, 2, 3, 4 P(X=x) 0.1, 0.35, 0.25, 0.2, 0.1

0.027

The table of data obtained from WWW.BASEBALL-ALMANAC.COM shows hit information for four well known baseball players. Suppose that one hit from the table is randomly selected. Find P(hit was a Home Run|The hit was made by Ty Cobb ).

0.271

The table of data obtained from WWW.BASEBALL-ALMANAC.COM shows hit information for four well known baseball players. Suppose that one hit from the table is randomly selected. Find P(hit was made by Hank Arron|The hit was a Single).

0.17

The table shows a random sample of musicians and how they learned to play their instruments. Find P(musician is a female AND had private instruction).

0.18

The table shows a random sample of musicians and how they learned to play their instruments. Find P(musician is a male AND had studied in School).

0.7851

There are 4 accidents, on average, at an intersection. Assume the variable follows a Poisson distribution. Find the probability that there will be 5 or less accidents at this intersection. (That is, find P(X ≤ 5)) (round to 4 decimal places) Answer:

0.25

There are 4 answers for a single question on the exam and only one answer is correct. If a student guesses the answer for this question, what is the probability that the student selects the correct answer? (round to 2 decimal places) Answer:

0.8774

There are 6.5 accidents, on average, at an intersection. Assume the variable follows a Poisson distribution. Find the probability that there will be 9 or less accidents at this intersection. (That is, find P(X≤9) (round to 4 decimal places) Answer:

0.0185

There are on average 5 old growth Sitka Spruce trees per 1/8 of an acre in a local forest. Find the probability that that there are exactly 30 Sitka Spruce trees in 1 acre in a remote part of the forest that is scheduled to be logged next year. Round answer to 4 decimal places. Answer:

Classical probability

What type of probability uses sample spaces to determine the numerical probability that an event will occur?

Probabilities must be nonnegative

Which of the following statements are true?

0.125

You see a game at a local fair. You have to throw a dart at a color wheel. Each section on the color wheel is equal in area. Let B = the event of landing on blue. Let R = the event of landing on red. Let G = the event of landing on green. Let Y = the event of landing on yellow. If you land on Y, you get the grand prize.

Yes

Does the following table represent a valid discrete probability distribution? X -5, -2.5, 0, 2.5, 5 P(X=x) 0.05, 0.25, 0.32, 0.18, 0.2

No

Does the following table represent a valid discrete probability distribution? X 1, 2, 3, 4, 5 P(X=x) 0.11, 0.06, 0.25, 0.41, 0.51

No

Does the following table represent a valid discrete probability distribution? X 1, 2, 3, 4, 5 P(X=x) 0.16, 0.01, 0.25, 0.11, 0.66

0.1944

Find the probability of rolling a sum of two dice that is a 7 or a 12. Round answer to 4 decimal places. Answer:

0.7680

A bank gets an average of 11 customers per hour. Assume the variable follows a Poisson distribution. Find the probability that there will be 9 or more customers at this bank in one hour. (That is, find P(X ≥ 9)) (round to 4 decimal places) Answer:

0.7576

A bank gets an average of 12 customers per hour. Assume the variable follows a Poisson distribution. Find the probability that there will be 10 or more customers at this bank in one hour. (That is, find P(X≥10) (round to 4 decimal places) Answer:

0.8815

A bank gets an average of 15 customers per hour. Assume the variable follows a Poisson distribution. Find the probability that there will be 11 or more customers at this bank in one hour. (That is, find P(X ≥ 11) (round to 4 decimal places) Answer:

0.0722

A bank gets an average of 8 customers per hour. Assume the variable follows a Poisson distribution. Find the probability that there will be 11 customers at this bank in one hour. (That is, find P(X=11) (Round answer to 4 decimal places) Answer:

60949324800

A baseball team has a 20-person roster. A batting order has nine people. How many different batting orders are there? Answer:

0.36

A box is filled with several party favors. It contains 12 hats, 15 noisemakers, 10 finger traps, and 5 bags of confetti. Let H = the event of getting a hat. Let N = the event of getting a noisemaker. Let F = the event of getting a finger trap. Let C = the event of getting a bag of confetti. Find P(N).

0.15

A jar of 150 jelly beans contains 22 red jelly beans, 38 yellow, 20 green, 28 purple, 26 blue, and the rest are orange. Let B = the event of getting a blue jelly bean Let G = the event of getting a green jelly bean. Let O = the event of getting an orange jelly bean. Let P = the event of getting a purple jelly bean. Let R = the event of getting a red jelly bean. Let Y = the event of getting a yellow jelly bean. Find P(R)

20

Approximately 10% of all people are left-handed. If 200 people are randomly selected, what is the expected number of left-handed people? Round to the whole number. Do not use decimals. Answer:

0.2711

Approximately 8% of all people have blue eyes. Out of a random sample of 20 people, what is the probability that 2 of them have blue eyes? Round answer to 4 decimal places. Answer:

0.7879

Approximately 8% of all people have blue eyes. Out of a random sample of 20 people, what is the probability that at most 2 of them have blue eyes? Round answer to 4 decimal places. Answer:

0.0479

Computer Help Hot Line receives, on average, 14 calls per hour asking for assistance. Assume the variable follows a Poisson distribution. What is the probability that the company will receive more than 20 calls per hour? Round answer to 4 decimal places. Answer:

0.2225

Computer Help Hot Line receives, on average, 14 calls per hour asking for assistance. What is the probability that the company will receive 3 calls in a 12 minute period? Round answer to 4 decimal places. Answer: