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# MATH 533 Final Exam 3 sets

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Author: Christine Farr
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1. (TCO A) The number of service calls made in the past 60 days by a sample of 20 technical representatives for AJ TECH is given below.
a. Compute the mean, median, mode, and standard deviation, Q1, Q3, Min, and Max for the above sample data on number of service calls made in the past 60 days.
b. In the context of this situation, interpret the Median, Q1, and Q3. (Points : 33)
2. (TCO B) Consider the following data on customers at an office supply store. These customers are categorized by their previous volume purchases and their age.
If you choose one customer at random, then find the probability that the customer
a. is a new customer.
b. is a high volume customer and is in the 40′s
c. is in the 20′s, given that the customer is low volume
3. (TCO B) DCW Chemical is planning to implement an acceptance sampling plan for raw materials. A random sample of 22 batches from a large shipment (having a large number of batches) is selected. If two or more of the 22 batches fail to meet specifications, then the entire shipment is returned. Otherwise, the shipment is accepted.
In a sample of 22 batches from a population that is 1% defective (1% of the batches fail to meet specifications), find the probability that
a. two or more batches fail to meet specifications.
b. exactly two batches fail to meet specifications.
c. fewer than two batches fail to meet specifications.
4. (TCO B) CJ Computer Disks stocks and sells recordable CDs. The monthly demand for these CDs is closely approximated by a normal distribution with a mean of 20,000 disks and standard deviation of 4,000 disks. CJ receives shipments from the supplier once per month (at the beginning of each month).
a. Find the probability that the demand for recordable CDs exceeds 30,000 for a particular month.
b. Find the probability that the demand for recordable CDs is between 12,000 and 18,000.
c. How large an inventory must CJ have available at the beginning of the month so that the probability of running out of recordable CDs (a stock out) during the month is no more than .05?
5. (TCO C) A tool manufacturing company wants to estimate the mean number of bolts produced per hour by a specific machine. A simple random sample of 9 hours of performance by this machine is selected and the number of bolts produced each hour is noted. This leads to the following results.
Sample Size = 9
Sample Mean = 62.3 bolts/hr
Sample Standard Deviation = 6.3 bolts/hr
a. Compute the 90% confidence interval for the average number bolts produced per hour.
b. Interpret this interval
c. How many hours of performance by this machine should be selected in order to be 90% confident of being within 1 bolt/hr of the population mean number of bolts per hour by this specific machine?
6. (TCO C) A clock company is concerned about errors in assembly of their custom made clocks. A random sample of 120 clocks from today’s production yields nine clocks with assembly errors.
a. Compute the 95% confidence interval for the percentage of clocks with assembly errors in today’s production
b. Interpret this confidence interval
c. How many clocks should be selected in order to be 95% confident of being within 2% of the population percentage of clocks with assembly errors in today’s production?
7. (TCO D) An article about women in business claims that 28% of all small businesses in the United States are owned by women. Sally Parks believes that this figure is overstated. A random sample of 2,000 small businesses is selected with 546 being owned by women. Does the sample data provide evidence to conclude that less than 28% of small businesses in the United States are owned by women (with a = .10)? Use the hypothesis testing procedure outlined below.

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