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}