# Math 221 all quizzes week 3, 5, 7 and week final exam

## MATH 221 Statistics for Decision Making – DeVry

MATH 221 Week 3 Quiz

** 1. Question : (TCO 1)** What method of data collection would you use to collect data for a study of the salaries of college professors at a particular college?

**2. Question : (TCO 2) **The chances of winning the California Lottery are 1 in 22 million. This statement describes

**3. Question : (TCO 2)** The colors of automobiles on a used car lot are

**4. Question : (TCO 1)** A lobbyist for a major airspace firm assigns a number to each legislator and then uses a computer to randomly generate ten numbers. The lobbyist contacts the legislators corresponding to these numbers. What sampling technique is used?

**5. Question : (TCO 2)** A recent survey by a national women’s association showed that the average salary of 3500 of its 65,000 membership was $73,000. This number is a

**6. Question : (TCO 2)** Which is used more often?

**7. Question : (TCO 2)** Suppose the standard deviation is 13.1. What is the variance?

**8. Question : (TCO 10)** These data represent the ages of drivers and the number of accidents reported for each age group in Pennsylvania for a selected year. (Age, Number of Accidents) (16, 6605), (17, 8932), (18, 8506), (19, 7349), (20, 6458), (21, 5974)

** 9. Question : (TCO 9)** A researcher found a significant relationship between a student’s IQ, a, the grade point average, b, and the score, y, on the verbal section of the SAT test. The relationship can be represented by the multiple regression equation y = 250 + 1.5a + 80b. Predict the SAT verbal score (to the nearest whole number) of a student whose IQ is 130 and grade point average is 2.2.

**10. Question : (TCO 9)** Interpret an r value of 0.11.

**11. Question : (TCO 3)** Use this table to answer the questions………….

1. Identify the class width.

2. Identify the midpoint of the first class.

3. Identify the class boundaries of the first class.

4. Give the relative frequency for each class.

**12. Question : (TCO 3)** The heights in inches of 18 randomly selected adult males in LA are listed as: 70, 69, 72, 57, 70, 66, 69, 73, 80, 68, 71, 68, 72, 67, 58, 74, 81, 72.

MATH 221 Week 5 Quiz

** 1. Question : (TCO 4)** Three members of a club will be selected to serve as officers. The first person selected will be president, the second person will be vice-president and the third will be secretary/treasurer. How many ways can these officers be selected if there are 30 club members?

** 2. Question : (TCO 4)** Which of the following cannot be a probability?

**3. Question : (TCO 4)** List the sample space of rolling a 6 sided die.

**4. Question : (TCO 4)** What is the probability of choosing a queen on the 2nd draw if the first was a queen (without replacement)?

**5. Question : (TCO 4) **A nursing class has 13 women and 18 men. If a student is chosen randomly to be the team leader, what is the probability the student is a woman?

**6. Question : (TCO 4)** Compute the following: 3! ÷ (0! * 3!)

**7. Question : (TCO 5)** Decide whether the experiment is a binomial, Poisson, or neither based on the information given. Each week a man plays a game in which he has a 21% chance of winning. The random variable is the number of times he wins in 64 weeks.

** 8. Question : (TCO 5)** Given a Poisson distribution with mean = 4. Find P(X < 3).

** 9. Question : (TCO 5)** Given the random variable X = {7, 8} with P(7) = 0.7 and P(8) = 0.3. Find E(X).

**10. Question : (TCO 5)** If X = {-1, 12, 3, -4} and P(-1) = 0.3, P(12) = 0.1, P(3) = 0.2, and P(-4) = 0.4, can distribution of the random variable X be considered a probability distribution?

**11. Question : (TCO 5)** If X = {2, 6, 10, 14} and P(2) = 0.2, P(6) = 0.3, P(10) = 0.4, and P(14) = 0.1, can distribution of the random variable X be considered a probability distribution?

** 12. Question : (TCO 5)** The number of shoes in your closet represents what kind of distribution?

** 13. Question : (TCO 5)** Your baby’s height represents what kind of distribution?

**14. Question : (TCO 5)** The amount of posts in our class at a given time represents what kind of distribution?

**Explanatory**

**1.Question : (TCO 5)** We have a binomial experiment with p = 0.4 and n = 2.

(1) Set up the probability distribution by showing all x values and their associated probabilities.

(2) Compute the mean, variance, and standard deviation.

** 2.Question : (TCO 4)** What is the probability that the student is a sophomore given he doesn’t carry a credit card?

**3.Question : (TCO 4)** Some students were asked if they carry a credit card. Here are the responses.

**4.Question : (TCO 4)** What is the probability that the student is a sophomore and doesn’t carry a credit card?

MATH 221 Week 7 Quiz

**1. Question : (TCO 6)** In the standard normal distribution, the standard deviation is always

**2. Question : (TCO 6)** The area under a normal curve with mu = 8 and sigma = 3 is

**3. Question : (TCO 6)** If Larry gets a 70 on a physics test where the mean is 65 and the standard deviation is 5.8, where does he stand in relation to his classmates?

**4. Question : (TCO 6)** In a normal distribution with mu = 25 and sigma = 6, what number corresponds to z = 3?

**5. Question : (TCO 6) **Let’s assume you have taken 100 samples of size 64 each from a normally distributed population. Calculate the standard deviation of the sample means if the population’s variance is 49.

** 6. Question : (TCO 6)** The area to the left of ‘z’ is 0.9976. What z-score corresponds to this area?

**7. Question : (TCO 6)** Find P(9 < x < 22) when mu = 20 and sigma = 5.

**8. Question : (TCO 7)** What is the critical z-value that corresponds to a confidence level of 86%?

** 9. Question : (TCO 7)** Compute the population mean margin of error for a 90% confidence interval when sigma is 4 and the sample size is 36.

**10. Question : (TCO 7)** A standard IQ test has a mean of 98 and a standard deviation of 16. We want to be 99% certain that we are within 8 IQ points of the true mean. Determine the sample size.

** 11. Question : (TCO 7)** A private medical clinic wants to estimate the true mean annual income of its patients. The clinic needs to be within $500 of the true mean. The clinic estimates that the true population standard deviation is around $2,300. If the confidence level is 95%, find the required sample size in order to meet the desired accuracy.

**12. Question : (TCO 7)** An auditor wants to estimate what proportion of a bank’s commercial loan files are incomplete. The auditor wants to be within 10% of the true proportion when using a 95% confidence level. How many files must the auditor sample? No estimate of the proportion is available, so use 0.5 for the population proportion.

**Explanatory **

**1. Question : (TCO 7) **Interpret a 95% confidence interval of (3.355, 3.445) for the population mean.

**2. Question : (TCO 7)** A nursing school wants to estimate the true mean annual income of its alumni. It randomly samples 200 of its alumni. The mean annual income was $52,500 with a standard deviation of $1,800. Find a 95% confidence interval for the true mean annual income of the nursing school alumni. Write a statement about the confidence level and the interval you find.

**3. Question : (TCO 7)** An auditor wants to estimate what proportion of a bank’s commercial loan files are incomplete. The auditor randomly samples 60 files and finds 12 are incomplete. Using a 95% confidence interval, estimate the true proportion of incomplete files for ALL the bank’s commercial loans. Write a statement about the confidence level and the interval you find.

MATH 221 Week 8 Final Exam

**(TCO 9)**The annual Salary of an electrical engineer is given in terms of the years of experience by the table below. Find the equation of linear regression for the above data and obtain the expected salary for an engineer with 45 years of experience. Round to the nearest $100.**(TCO 5)**A company produces window frames. Based on a statistical analysis, we found that 15% of their product is defective. They have shipped 10 windows to one of their customers. The customer is worried about the probability of having defective frames. Choose the best answer of the following:**(TCO 5)**A test is composed of six multiple choice questions where each question has 4 choices. If the answer choices for each question are equally likely, find the probability of answering 3 OR 4 questions correctly.**(TCO 5)**It has been recorded that the average number of errors in a newspaper is 4 mistakes per page. What is the probability of having 1 or 2 errors per page?**(TCO 2)**The median height of the players on a high school basketball team is 68 inches. What does this tell you about the typical height of a player on this team?**(TCO 6)**Using the standard normal distribution, find the probability that z is greater than 1.78**(TCO 8)**The mean age of school bus drivers in Denver is claimed to be 56.9 years. A hypothesis test is performed at a level of significance of 0.01 with a P-value of 0.09. Choose the best interpretation of the hypothesis test.**(TCO 8)**A poll of U.S. health professionals revealed less than 82% would choose the same career. In a hypothesis test conducted at a level of significance of 1%, a P-value of 0.035 was obtained. Choose the best interpretation of the hypothesis test.**(TCO 2)**You are going to take a statistics class next session. You have two professors to choose from. Both professors have a mean performance evaluation score of 3.56 out of 4. Professor A has a standard deviation of .86 while Professor B has a standard deviation of .51. You want to choose the better professor because math is a challenge for you, who do you choose?**(TCO 4)**A travel agency offers 4 different vacation packages to Europe. Their net profit for package 1 is $500, for package 2 it is $750, for package 3 it is $900, and for package 4 it is $1,500. From past experience they know that 20% of their customers purchase package 1, 15% of their customers purchase package 2, 40% of their customers purchase package 3 and 25% of their customers purchase package 4. Find the expected value or average profit per customer and determine how much profit they should expect if 10 people purchase one of their European vacation packages.**(TCO 3)**The ages of 25 employees in a company are listed below: Use the stem & leaf plot to determine the shape of the distribution. Choose the best answer.**(TCO 1**) A statistician is considering using a 99% confidence interval for a study instead of a 95% confidence interval. What happens to the required sample size if the confidence level is increased from 95% to 99% and the same error is required in each case?**(TCO 6)**Scores on an assessment exam at a private school are normally distributed, with a mean of 75 and a standard deviation of 11. Any student who scores in the top 7% is eligible for a scholarship. What is the lowest whole number score you can earn and still be eligible for a scholarship?**(TCO 5)**A shipment of 40 computers contains five that are defective. How many ways can a small business buy three of these computers and receive no defective ones?**(TCO 6)**The time required to make 1100 gallons of synthetic rubber at a plant in South America in a recent year was normally distributed with a mean of 16 hours and a standard deviation of 3 hours. What is the probability that it will take more than 19 hours to make 1100 gallons of synthetic rubber?**(TCO 10)**The annual rice yield (in pounds), is given by the equation y-hat = 859 + 5.76a + 3.82b, where ‘a’ is the number of acres planted (in thousands), and ‘b’ is the number of acres harvested (in thousands). Predict the annual rice yield (in pounds) when the number of acres planted is 2550 (in thousands) and the number of acres harvested is 2245 (in thousands).**(TCO 9)**Describe the correlation in this graph.**(TCO 8)**For the following statement, write the null hypothesis and the alternative hypothesis. Then, label the one that is the claim being made.**(TCO 11)**A 15-minute Oil and Lube service claims that their average service time is no more than 15 minutes. A random sample of 35 service times was collected, and the sample mean was found to be 16.2 minutes, with a sample standard deviation of 3.5 minutes. Is there evidence to support, or to reject the claim at the alpha = 0.05 level? Perform an appropriate hypothesis test, showing the necessary calculations and/or explaining the process used to obtain the results. Writing the formal conclusion is an important part of the process.**(TCO 5)**The probability that a house in an urban area will be burglarized is 5%. If 50 houses are randomly selected, what is the probability that one of the houses will be burglarized? (a) Is this a binomial experiment? Explain how you know. (b) Use the correct formula to find the probability that, out of 50 houses, exactly 4 of the houses will be burglarized. Show your calculations or explain how you found the probability.**(TCO 6)**The average monthly gasoline purchase for a family with 2 cars is 90 gallons. This statistic has a normal distribution with a standard deviation of 10 gallons. A family is chosen at random.**(TCO 8)**An engineering firm is evaluating their back charges. They originally believed their average back charge was $1800. They are concerned that the true average is higher, which could hurt their quarterly earnings. They randomly select 40 customers, and calculate the corresponding sample mean back charge to be $1950. If the standard deviation of back charges is $500, and alpha = 0.04, should the engineering firm be concerned? Perform an appropriate hypothesis test, showing the necessary calculations and/or explaining the process used to obtain the results.**(TCO 7)**A marketing firm wants to estimate the average amount spent by patients at the hospital pharmacy. For a sample of 200 randomly selected patients, the mean amount spent was $92.75 and the standard deviation $13.10. (a) Find a 95% confidence interval for the mean amount spent by patients at the pharmacy. Show your calculations and/or explain the process used to obtain the interval. (b) Interpret this confidence interval and write a sentence that explains it.**(TCO 7)**A drug manufacturer wants to estimate the mean heart rate for patients with a certain heart condition. Because the condition is rare, the manufacturer can only find 15 people with the condition currently untreated. From this small sample, the mean heart rate is 92 beats per minute with a standard deviation of 8. (a) Find a 98% confidence interval for the true mean heart rate of all people with this untreated condition. Show your calculations and/or explain the process used to obtain the interval. (b) Interpret this confidence interval and write a sentence that explains it.**(TCO 2)**The heights of 10 sixth graders are listed in inches: {50, 62, 54, 57, 60, 57, 53, 57, 59, 58}. (a) Find the mean, median, mode, sample variance, and range. (b) Do you think that this sample might have come from a normal population? Why or why not?