Business Stat Mid-Term Set 2

The length of time it takes shoppers to find a parking spot in the mall parking lot follows a normal distribution with a mean of 3.5 minutes and a standard deviation of 1 minute. Find the probability that a randomly selected shopper will find a parking spot in the mall parking lot in less than 3 minutes.

0.3085

The probability that a new advertisement will increase sales is 0.80. The probability that the cost of the new ad will be kept within budget is 0.40. If the two events are independent, the probability that the cost is kept within budget and the new ad will increase sales is:

0.32

The manager of Ardmore Pharmacy knows that 50% of the customers entering the store buy prescription drugs, 65% buy over‐the‐counter drugs and 18% buy both types of drugs. What is the probability that a randomly selected customer will buy at least one of these two types of drugs or both?

0.97

For sample sizes greater than 30, the sampling distribution of the mean is approximately normally distributed

regardless of the shape of the population.

The size of the standard error is affected by the standard deviation of the population and

the sample size.

The mean fill of containers of sugar is 16.0 ounces with a population standard deviation of 1.5 ounces. Samples of size 4 are taken from the population of all containers of sugar. Find the probability that a given sample mean, x , will exceed 17 ounces. Assume the population is normal.

0.0918

The population of monthly cell phone plans cost an average of $75 with a standard deviation of $12. Find the probability that the mean of a sample of 30 observations taken from this population will between $77 and $80.

0.1701

Identify the correct statement.

If a population mean is equal to 200, the sample mean for a random sample selected from the population is about as likely to be higher or lower than 200.

Which of the following is true regarding the sampling distribution of the mean for a large sample size (n > 30)? Assume the population distribution is positively skewed.

It has the same mean as the population, but a different shape and standard deviation.

Whether you are a U.S. citizen. Your marital status. Heidi's favorite brand of tennis balls.

Nominal

The distribution of ages of frequent individuals with text messaging phone plans is positively skewed with a mean age of 22 and a standard deviation of 4.45. If we repeatedly sampled n = 100 consumers from the population, describe the sampling distribution of the sample mean.

Normal with mean = 22 and standard deviation = 0.445

On Tuesday, December 30, 2008 (before the NFL championship playoffs), the Cal Sports Book gave the Arizona Cardinals 25-1 odds against winning the Super Bowl, and the Pittsburgh Steelers 4-1 odds against winning the Super Bowl. What is the implied probability of the Steelers' victory?

P(Steelers' win) = 1/(1+4) = 0.20

The number of cars parked in a certain parking lot at any given time. The amount of time you spent last week on your homework. Lily's travel time from her dorm to the student union on campus.

Ratio

A bottling company fills bottles of IBC root beer. The weights of the root beer are normally distributed with a mean of 12 fl oz. and a standard deviation of 0.1 fl oz. Find the probability that a bottle of root beer will have a weight greater than 12.5 fl oz.

approximately 0.

A supermarket mailed a survey to 500 nearby residents selected at random. The sample was designed to include 125 residents randomly selected from each of the types of housing: single‐home, condo, apartments, and townhomes Which sampling technique was used?

Stratified random sampling.

Suppose P(A) = 0.50, P(B) = 0.40, and P(B|A) = 0.30. a. Find P(A ∩ B) b. Find P(A ∪ B) c. Find P(A|B)

a. P(A ∩ B) = P(B|A)P(A) = 0.30(0.50) = 0.15 b. P(A ∪ B) = P(A) + P(B) - P(A ∩ B) = 0.50 + 0.40 - 0.15 = 0.75 c. P(A|B) = P(A ∩ B)/P(B) = 0.15/0.40 = 0.375

A survey of a magazine's subscribers indicates that 50% own a home (event H), 80% own a car (event C), and 90% of the homeowners who subscribe also own a car, P(C|H) = 0.90. a. What is the probability that a subscriber owns both a car and a house? b. What is the probability that a subscriber owns a car or a house, or both? c. What is the probability that a subscriber owns neither a car nor a house?

a. P(C ∩ H) = P(C|H) P(H) = 0.45 b. P(C ∪ H) = P(C) + P(H) - P(C ∩ H) = 0.80 + 0.50 - 0.45 = 0.85 c. P(CC ∩ HC) = 1‐ P(C ∪ H) = 1 - 0.85 = 0.15

. The probability that house sales will increase in the next 6 months (event H) is estimated to be 0.30. The probability that the interest rates on housing loans will go up in the same period (event I) is estimated to be 0.75. The probability that house sales or interest rates will go up during the next 6 months is estimated to be 0.90. a. What is the probability that both house sales and interest rates will increase during the next six months? b. What is the probability that neither house sales nor interest rates will increase during the next six months?

a. P(H ∩ I) = P(H) + P(I) - P(H ∪ I) = 0.30 + 0.75 - 0.90 = 0.15 b. P(HC ∩ IC) = 1 - P(H ∪ I) = 1‐ 0.90 = 0.10

Which of the following is an example of a nonsampling error?

a. Some incorrect responses are recorded. b. Responses are not obtained from all members of the sample. c. Some members of the target population cannot possibly be selected for the sample. d. All of the above. <-

Which of the following statements is correct regarding the design of a good survey?

a. The questions should be kept as short as possible. b. A mixture of dichotomous (yes|no), multiple‐choice, and open‐ended questions may be used. c. Leading questions must be avoided. d. All of the above. <-