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# MATH 533 Week 3 Homework (New)

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1.      The mean gas mileage for a hybrid car is 56 miles per gallon. Suppose that the gasoline mileage is approximately normally distributed with a standard deviation of 3.3 miles per gallon.

2.      The ages of a group of 50 women are approximately normally distributed with a mean of 49 years and a standard deviation of 5 years. One woman is randomly selected from the group, and her age is observed.

3.      Resource Reservation Protocol (RSVP) was originally designed to establish signaling links for stationary networks. RSVP was applied to mobile wireless technology. A simulation study revealed that the transmission delay (measured in milliseconds) of an RSVP linked wireless device has an approximate normal distribution with mean µ = 49.5 milliseconds and milliseconds. Complete parts a and b.

4.      Almost all companies utilize some type of year-end performance review for their employees. Human Resources (HR) at a university’s Health Science Center provides guidelines for supervisors rating their subordinates. For example, raters are advised to examine for tendency to be either too lenient or too harsh. According to HR, “if you have this tendency, consider using a normal distribution—10% of employees (rated) exemplary, 20% distinguished, 40% competent, 20% marginal, and 10% unacceptable. “Suppose you are rating an employee’s performance on a scale of 1 (lowest) to 100 (highest). Also, assume the ratings follow a normal distribution with a mean of 49 and a standard deviation of 15. Complete parts a and b.

5.      Personnel tests are designed to test a job applicant’s cognitive and/or physical abilities. A particular dexterity test is administered nationwide by a private testing service. It is known that for all tests administered last year, the distribution of scores was approximately normal with mean 78 and standard deviation 6.6.

6.      Before negotiating a long-term construction contract, building contractors must carefully estimate the total cost of completing the project. At a certain university, a contractor proposed a model for total cost of a long-term contract based on the normal distribution. For one particular construction contract, the university assumed total cost, x, to be normally distributed with mean \$860,000 and standard deviation \$180,000. The revenue, R, promised to the contractor is \$1,000,000.

7.      The characteristics of an industrial filling process in which an expensive liquid is injected into a container was investigated. The quantity injected per container is approximately normally distributed with mean 10 units and standard deviation 0.02 units. Each unit of fill costs \$10 per unit. If a container contains less than 10 units (that is, is underfilled), it must be reprocessed at a cost of \$14. A property filled container sells for \$125. Complete parts a through c.

8.      A random sample of n = 100 observations is drawn from a population with mean equal to 46 and a standard deviation to 40.

9.      A random sample of n = 64 observations is drawn from a population with a mean equal to 21 and a standard deviation equal to 16.

10.  The average salary for a certain profession is \$74,500. Assume that the standard deviation of such salaries is \$32,500. Consider a random sample of 52 people in this profession and let x represent the mean salary for the sample.

11.  Some students paid a private tutor to help them their results on a certain mathematical test. These students had a mean change in score of +17 points, with a standard deviation of 69 points. In a random sample of 100 students who pay a private tutor to help them improve their results, what is the likelihood that change in the sample mean score is less than 10 points?

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