SCMT 303 Midterm 1

For some value of​ Z, the value of the cumulative standardized normal distribution is 0.2090. What is the value of​ Z? Round to two decimal places.

-0.81

In a particular​ game, the probability of winning $142 is 1/36 and the probability of losing $10 is 35/36. What is the expected value after playing this​ game? Round to the nearest cent.

-$5.78

Let X represent the amount of time until the next student will arrive in the library parking lot at the university. If we know that the distribution of arrival time can be modeled using an exponential distribution with a mean of 4 minutes​ (i.e. the mean number of arrivals is​ 1/4 per​ minute), find the probability that it will take more than 10 minutes for the next student to arrive at the library parking lot. Round to six decimal places.

.082085

A cat has a litter of 7 kittens. Find the probability that exactly 5 of the little furballs are female. Assume that male and female births are equally likely. Round to five decimal places.

.16406

A small business just leased a new presentation equipment and a color laser printer for three years. The service contract for the computer offers unlimited repairs for a fee of​ $100 a year plus a​ $25 service charge for each repair needed. The​ company's research indicates that during a given year​ 86% of these computers need no​ repairs, 9% need to be repaired​ once, 4%​ twice, 1% three​ times, and none required more than three repairs. Find the expected number of repairs for this kind of computer per year.

.20 repairs

What is the probability that 6 rolls of a fair die will show four exactly 2 ​times? Round to five decimal places.

.20094

If we know that the length of time it takes a college student to find a parking spot in the library 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 college student will find a parking spot in the library parking lot in less than 3 minutes. Round to four decimal places.

.3085

The value of the cumulative standardized normal distribution at Z is 0.6255. What is the value of​ Z? Round to two decimal places.

.32

A company that receives most of its orders by telephone conducted a study to determine how long customers were willing to wait on hold before ordering a product. The length of waiting time was found to be a variable best approximated by an exponential distribution with a mean length of waiting time equal to 3 minutes​ (i.e. the mean number of calls answered in a minute is​ 1/3). What proportion of customers having to hold more than 1.5 minutes will hang up before placing an​ order? Round to five decimal places.

.60653

The probabilities that a batch of 4 computers will contain​ 0, 1,​ 2, 3, and 4 defective computers are 0.4521​, 0.3970​, 0.1307​, 0.0191​, and 0.0010 respectively. Find the standard deviation of the random variable. Round to two decimal places

.77

Suppose the time it takes for customer representatives to diagnose and fix computer problems is uniformly distributed from 10 to 120 minutes. What is the probability that it takes longer than 90 minutes to diagnose and fix a computer​ problem?

0.27

The value of the cumulative standardized normal distribution at 1.5X is 0.9332. What is the value of​ X? Round to two decimal places.

1.00

Suppose X has a Poisson distribution with parameter λ=1.500. Find the standard deviation of X. Round to three decimal places.

1.225

If n=10 and π=​0.70, then what is the standard deviation of the binomial​ distribution? Round to two decimal places.

1.45

In one​ town, the number of burglaries in a week has a Poisson distribution with parameter λ=2.6. Let X denote the number of burglaries in the town in a randomly selected week. Find the standard deviation of X. Round to three decimal places.

1.612

Assume that a set of test scores in an Introduction to Finance class is normally distributed with a mean of 72 and a standard deviation of 8. Use the​ 68-95-99.7 Rule to find the percentage of scores greater than 88.

2.5%

The time it takes to process phone orders in a small​ florist/gift shop is normally distributed with a mean of 6 minutes and a standard deviation of 1.24 minutes. What cutoff values would separate the​ 16% of orders that take the least time to​ process?

4.76 minutes

The owner of a fish market determined that the mean weight for a catfish is 3.2 pounds with a standard deviation of 0.8 pound. A citation catfish should be one of the top​ 2% in weight. Assuming the weights of catfish are normally​ distributed, at what weight​ (in pounds) should the citation designation be​ established? Round to two decimal places.

4.84 pounds

The amount of corn chips dispensed into a 48​-ounce bag by the dispensing machine has been identified as possessing a normal distribution with a mean of 48.5 ounces and a standard deviation of 0.2 ounce. What chip amount represents the 67th percentile for the bag weight​ distribution? Round to the nearest thousandth.

48.588 oz

A company that receives most of its orders by telephone conducted a study to determine how long customers were willing to wait on hold before ordering a product. The length of waiting time was found to be a variable best approximated by an exponential distribution with a mean length of waiting time equal to 3 minutes​ (i.e. the mean number of calls answered in a minute is​ 1/3). Find the waiting time at which only​ 10% of the customers will continue to hold. Round to one decimal place.

6.9 minutes

A North American mole weighs an average of 3.5 ounces​ (oz.) with a standard deviation of 0.9 oz. and a distribution that is approximately normal. In what percentile is the weight of a mole that weighs 4.25​ oz.?

79.8%

Assume that a set of test scores in an Introduction to Finance class is normally distributed with a mean of 72 and a standard deviation of 8. Use the​ 68-95-99.7 Rule to find the percentage of scores between 64 and 88.

81.5%

Based on data collected from its production​ processes, Crosstiles Inc. determines that the breaking strength of its most popular porcelain tile is normally distributed with a mean of 400 pounds per square inch​ (psi) and a standard deviation of 12.5 psi. Based on the​ 68-95-99.7 Rule, about what percent of its popular porcelain tile will have breaking strengths between 375 and 425​ psi?

95%

The local police department must​ write, on​ average, 5 tickets a day to keep department revenues at budgeted levels. Suppose the number of tickets written per day follows a Poisson distribution with a mean of 6.5 tickets per day. Interpret the value of the mean.

A. The number of tickets that is written most often is 6.5 tickets per day. B. The mean has no interpretation since 0.5 ticket can never be written. C. If we sampled all​ days, the arithmetic average or expected number of tickets written would be 6.5 tickets per day. D. Half of the days have less than 6.5 tickets​ written, and half of the days have more than 6.5 tickets written.

A professor​ receives, on​ average, 24.7 emails from students the day before the midterm exam. To compute the probability of receiving at least 10 emails on such a​ day, he will use what type of probability​ distribution?

A. binomial distribution B. Poisson distribution C. hypergeometric distribution D. none of the above

A stock analyst was provided with a list of 25 stocks. He was expected to pick 3 stocks from the list whose prices are expected to rise by more than​ 20% after 30 days. The prices of only 5 stocks would rise by more than​ 20% after 30 days. If he randomly selected 3 stocks from the​ list, he would use what type of probability distribution to compute the probability that all the chosen stocks would appreciate more than​ 20% after 30​ days?

A. binomial distribution B. Poisson distribution C. hypergeometric distribution D. none of the above

From an inventory of 48 new cars being shipped to local​ dealerships, corporate reports indicate that 12 have defective radios installed. The sales manager of one dealership wants to predict the probability out of the 8 new cars it just received​ that, when each is​ tested, no more than 2 of the cars have defective radios. What type of probability distribution will most likely be used to analyze the number of cars with defective​ radios?

A. binomial distribution. B. Poisson distribution. C. hypergeometric distribution. D. none of the above

What does the connotation​ "expected value" or​ "expected gain" from playing roulette at a casino​ mean?

A. the amount you expect to​ "gain" on a single play B. the amount you should expect to gain if you are lucky C. the amount you need to​ "break even" over many plays D. the amount you expect to​ "gain" in the long run over many plays

Which of these statements is true about a binomial​ distribution?

A. the probability of event of interest π is stable from trial to trial B. the number of trials n must be at least 30 C. the variable X is continuous D. the results of one trial are dependent on the results of the other trials

A lab orders 100 rats a week for each of the 52 weeks in the year for experiments that the lab conducts. Prices for 100 rats follow the distribution in the table. ​Price: ​$10.00 ​$12.50 ​$15.00 ​Probability: 0.35 0.40 0.25 How much should the lab budget for next​ year's rat orders​ be, assuming this distribution does not​ change?

A. ​$650 B. ​$637 C. ​$520 D. ​$780

Which of the following about the normal distribution is not​ true?

A. ​Theoretically, the​ mean, median, and mode are the same. B. Its parameters are the​ mean, μ​, and standard​ deviation, σ. C. About​ 2/3 of the observations fall within ±1 standard deviation from the mean. D. It is a discrete probability distribution.

Whenever π=​0.5, what will the shape of the binomial distribution​ be?

A. ​right-skewed B. always symmetric C. symmetric only if n is large D. ​left-skewed

Suppose a coin is tossed four times. Let X denote the total number of tails obtained in the four tosses. What are the possible values of the random variable​ X?

A. ​{1,2,3} B. ​{1,2,3,4} C. ​{HHHH, HHHT,​ HHTH, HHTT,​ HTHH, HTHT,​ HTTH, HTTT,​ THHH, THHT,​ THTH, THTT,​ TTHH, TTHT,​ TTTH, TTTT} D. ​{0,1,2,3,4}

An insurance company has called a consulting firm to determine if the company has an unusually high number of false insurance claims. It is known that the industry proportion for false claims is​ 3%. The consulting firm has decided to randomly and independently sample 100 of the​ company's insurance claims. They believe the number of these 100 that are false will yield the information the company desires. What type of probability distribution will the consulting firm most likely employ to analyze the insurance​ claims?

A. Poisson distribution B. hypergeometric distribution C. binomial distribution D. none of the above

Suppose you sample one value from a uniform distribution with a=0 and b=20. a. What is the probability that the value will be between 12 and 17? b. What is the probability that the value will be between 4 and 7? c. What is the​ mean? d. What is the standard​ deviation?

a. The probability that the value will be between 12 and 17 is .25 b. The probability that the value will be between 4 and 7 is .15 c. The mean of the given uniform distribution is μ=10. d. The standard deviation of the given uniform distribution is σ=5.7735

For a randomly selected student in a particular high​ school, let Y denote the number of living grandparents of the student. What are the possible values of the random variable​ Y?

{0,1,2,3,4}