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TESTIII-BANA2081-001Spring2020.docx

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Spring 2020

BANA 2081-001: Business Analytics I

TEST III Due Date: 04/17/2020 via Canvas Only

NAME_______________________________________________________

NOTE: SHOW WORKING TOWARDS ANSWERS WHERE NECESSARY

1. (a) (12 points) In manufacturing disposable diapers, a diaper that weighs less than 18 ounces is considered defective. Historically, diaper weight has followed a normal distribution with an average 18.5 ounces and standard deviation of 2 ounces. Using this historical results, what percent of diapers are defective?

(b)(12 points) The mean preparation fee H&R Block charged retail customers last year was $183. Use this price as the population mean and assume the population standard deviation of preparation fees is $50. What is the probability that the mean price for a sample of 50 H&R Block retail customers is within $8 of the population mean?

2.(a)(6 points) What are the two methods of estimation?

(b) (6 points) Give two characteristics of the normal distribution.

3. (a) (12 points) The following random sample was selected from a distribution: 4, 6, 3, 5, 9, 3.

The standard deviation for the sample is 2.2804. Construct a 99% confidence interval for population mean .

(b) (12 points) First year students in a large class were asked “About how many minutes they study on a typical weeknight?” The mean response of a sample of 463 students was minutes. Suppose we know that the study time follows a normal distribution with variance, in the population of all first-year students at this university.

Use the survey to construct a 95% confidence interval for the mean study time of all first-year students.

4. (a) (8 points) Slater customers are charged for the amount of salad they take. Sampling suggests that the amount of salad taken is uniformly distributed between 5 ounces and 15 ounces.

(i) (2 points) Write down the probability density function for this distribution.

(ii) (2 points) Compute the expected value of the random variable.

(iii) (2 points) Draw a graph for this probability density function.

(iv) (2 points) What is the probability that a customer will take between 12 and 15 ounces of salad?

(b) (7 points) In developing patient appointment schedules, a medical center wants to estimate the mean time that a staff member spends with each patient. How large a sample should be taken if the desired margin of error is two minutes at a 95% confidence level? Use a planning value for the population standard deviation of eight minutes.

CIRCLE THE BEST ANSWER

1. (4 points) The standard normal distribution has a mean of 1 and a standard deviation of 0.

(A) True

(B) False

2. (4 points) In constructing a confidence interval for the mean, when the population standard deviation is unknown, then we use

(A) t-distribution

(B) normal distribution

(D) Poisson distribution

3. (4 points) A normal distribution has a mean of 10 and a standard deviation of 2. Then the mode of this normal distribution is

(A) 2

(B) 10

(D) 100

4. (4 points) The method of sampling where the person most knowledgeable of the subject of study selects the elements of the population that he or she feels are the most representative of the population is

(A) Stratified Random Sampling

(B) Cluster Sampling

(D) Systematic Sampling

5. (4 points) All are properties of a point estimator except

(A) Biased

(B) Unbiased

(D) Consistency

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