Stats 2

The weight of cats is a continuous random variable and has a normal distribution with a mean of 10.27 pounds and a standard deviation of 4.26 pounds. What is the probability that a randomly chosen cat weighs exactly 11.327 pounds? You can round your answer to two decimal places.

0

EXTRA CREDIT #1: This question is worth up to 40 points extra credit, but it will be graded manually. This means that it might show temporarily with a score of zero even if your answer is correct. Customers arrive at your store based on a Poisson process with a mean of 4 arrivals per hour. It is currently 3:00 pm and the last customer came in at 2:15 pm. What is the probability that no new customers will arrive before 3:15 pm? Include 4 places past the decimal in your answer.

0.0183

EXTRA CREDIT #3: This question is worth up to 40 points extra credit, but it will be graded manually. Therefore, it may show temporarily with a score of zero even if your answer is correct. A deck of 52 playing cards consists of four suits, each with thirteen cards. In the game called bridge, a hand consists of thirteen cards selected randomly without replacement. What is the probability that a bridge hand will have exactly 7 cards in the same suit? Round your answer to three decimal places.

0.0353

Based on historical statistics, a climatologist has determined that the probability of rain on Feb. 1 in San Francisco is 0.4. Use the normal approximate to the binomial to calculate the probability that it will rain in San Francisco on exactly 40 of the next 100 Feb. 1 dates. Round your answer to four decimal places.

0.0813

Fortune magazine publishes an annual list of the 500 largest companies in the United States. In the 2018 rankings, 49 of these companies had their headquarters in California. If you pick a company at random from this 2018 list, what is the probability that the company you pick has headquarters in California? You must include three places past the decimal in your answer. Do not give your answer as a percentage.

0.098

The average unemployment rate in California in January 2019 was 4.2%. Assume that 400 employable people in California were selected randomly in January 2019. What is the expected value of the number of people in the sample who were unemployed? Round your answer to one decimal point.

16.8

You study the number of cups of coffee consumer per day by students and discover that it follows a discrete uniform probability distribution with possible values for x of 0, 1, 2 and 3. What is the expected value of the random variable x? (You can round your final answer to two decimals, but do not do any rounding when you are doing the intermediate calculations.)

1.5

A State issues car license plate with one number, followed by three letters, followed by three numbers. Letters and numbers can repeat multiple times in the same license plate. For example, possible license plates are 0ABC123 and 2BBB222. How many different license plates are possible? (Hint: Remember that there are 26 letters in the alphabet and 0 is a valid number.) Do not include commas in your answer.

175,760,000

When probabilities are assigned based on the assumption that all the possible outcomes are equally likely, the method used to assign the probabilities is called the Group of answer choices

classical method

The probability that a customer at your coffee shop will order decaf coffee is 0.40 and each customer's order is independent of every other customer's order. What is the probability that exactly 2 of the next 6 customers will order decaf? You can round your answer to two decimal points.

.31

Consider two events, event A and event B, with the following probabilities: P ( A ) = 0.80 P ( B ) = 0.50 If event A and event B are independent, then P ( A ∩ B ) = Include two places past the decimal in your answer.

.4

You take a census of cars in a parking lot and discover that the probability that a car in the parking lot is blue is 0.20 and the probability that the car is a Ford is 0.30. The probability that the car is both blue and a Ford is 0.10. What is the probability that a randomly selected car from the parking lot is either blue, or a Ford, or both? Include two places past the decimal in your answer.

.4

You are the sales manager for a large high-end clothing store. You have a total of 100 salespeople at the store, and 30 of them sold $1000 or less yesterday while the rest sold over $1000. Among the salespeople who sold $1000 or less, there is a probability of 0.30 that the salesperson is new on the job (less than one year of experience). Among the salespeople who sold over $1000 there is a probability of 0.10 that the salesperson is new on the job (less than one year of experience). Given that a salesperson is new on the job, what is the probability that the salesperson sold over $1000 yesterday? You can round your answer to two decimal places.

.44

If IQ test scores are normally distributed with a mean of 100 and a standard deviation of 15, what is the probability that a randomly selected person will have an IQ score greater than 115? You should provide four decimal points in your answer.

0.1587

The number of gallons of gasoline sold at your gas station on any one day has a (continuous) uniform distribution with a minimum of 500 and a maximum of 1500. What is the probability that you will sell more than 1300 gallons of gasoline on any particular day? You may round your answer to two decimal places.

0.2

A florist looks at his sales and discovers that the probability that a randomly selected flower sold is a rose is 0.40. The probability that a randomly selected flower sold is white is 0.10. The probability that a randomly selected flower sold is a white rose is 0.03. Given that a randomly selected flower sold is white, what is the probability that it is also a rose? You can round your answer to two decimal places.

0.3

EXTRA CREDIT #2: This question is worth up to 40 points extra credit, but it will be graded manually. This means it might show temporarily with a score of zero even if your answer is correct. I flip three fair coins, each with a 50-50 probability of getting heads or tails. I do not show you the results, but I tell you that at least one of the three coins shows heads. Given this information, calculate the conditional probability that exactly two of the three coins show heads. You can round your answer to two decimal places.

0.43

Assume that the mean debt for credit cards at your bank is $12,000. The population standard deviation is $4000 and the debt amounts have a normal distribution. What is the probability that the debt for one of your credit card holders is between $10,000 and $15,000? You should provide four numbers past the decimal point in your answer.

0.4649

In a normal probability distribution, what is the probability that x is greater than or equal to the mode? You may round your answer to two decimal places, but your answer must be exactly correct in order to get credit.

0.5

Bob Neverready has a portable TV. The TV uses two batteries and both of them are dead. Bob opens a new pack of six good batteries and dumps them on the table. Then he opens the TV and dumps the two dead batteries on the table with the good ones. The batteries get mixed up and Bob no longer knows which are which. (Has this ever happened to you?) If Bob picks two batteries off of the table at random and puts them into the TV, what is the probability that he chose two good batteries and that the TV will work? You can round your answer to three decimal places.

0.536

The mean number of users at an ATM is 3 per hour. Assuming that the users arrive according to a Poisson process, what is the probability that at least one user arrives during a particular hour? (Hint: Recall that "at least" means "greater than or equal to.") You may round your final answer to two decimal points.

0.95

You study the number of cups of coffee consumer per day by students and discover that it follows a discrete uniform probability distribution with possible values for x of 0, 1, 2 and 3. What is the standard deviation of the random variable x? (You can round your final answer to two decimals, but do not do any rounding when you are doing the intermediate calculations.)

1.12

The standard version of the game of poker is played with a deck of 52 different playing cards and a poker player is given 5 cards at random without replacement as a poker hand. The order in which the cards are chosen does not matter. How many different standard poker hands are possible? (Do not put any commas or decimals in your answer.)

2,598,960

Travelers arrive at an airport security line at an average rate of 49 per minute with a Poisson process. What is the standard deviation of the random variable that measures the number of arrivals per minute? You can round your answer to the nearest whole number.

7

You run an experiment where you weigh shipments of boxes from a warehouse. The random variable, x, is the number of pounds in the shipment. Is this random variable, x, discrete or continuous?

Continuous

How do you interpret f(x) for a discrete and a continuous random variable? Group of answer choices

For a discrete random variable it gives the probability that the random variable takes on the value of x and for a continuous random variable it gives the height of the probability density function.

During the past five years the probability that a California consumer has bought a burrito (event B) is 0.70 and the probability that a California consumer has bought a Honda (event H) is 0.10. The probability that a California consumer has bought both a burrito and and Honda in the past five years is 0.05. Are the purchases of burritos and Hondas in the past five years among California consumers independent events?

No, they are not independent events.

You are running an experiment with three mutually exclusive and exhaustive experimental outcomes: A, B and C. Which of the following is a possible set of probabilities for these outcomes?

P(A)=0.20 P(B)=0.00 P(C)=0.80

Continuing on with the previous question: The reason your answer to the previous question is correct is:

P(B|H) does not equal P(B)

You run an experiment where you weigh shipments of boxes from a warehouse. The random variable, x, is the number of pounds in the shipment. Identify the possible values that the random variable can assume. Give your answer as a mathematical expression based on x.

X>0