## (solution) 1) Personnel tests are designed to test a job applicant's

please answer the attached homework 6 questions

statistics homework

1)

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 71

and standard deviation 6.7.

a. A particular employer requires job candidates to score at least 76 on the dexterity test.

Approximately what percentage of the test scores during the past year exceeded 76?

b. The testing service reported to a particular employer that one of its job candidate's scores fell at

the 95th percentile of the distribution (i.e., approximately 95% of the scores were lower than

the candidate's, and only 5% werehigher). What was the candidate's score?

2)

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 \$870,000

and standard deviation \$180,000. The revenue, R, promised to the contractor is

\$1,000,000.

a. The contract will be profitable if revenue exceeds total cost. What is the probability that the

contract will be profitable for the contractor?

b. What is the probability that the project will result in a loss for the contractor?

c. Suppose the contractor has the opportunity to renegotiate the contract. What value of R should the

contractor strive for in order to have a 0.99

probability of making a profit? 3)

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 mean10

units and standard deviation 0.02 units. Each unit of fill costs \$30 per unit. If a container contains less

than 10 units (that is, is underfilled), it must be reprocessed at a cost of \$14. A properly filled container

sells for \$350.

a. Find the probability that a container is underfilled?

b. A container is initially underfilled and must be reprocessed. Upon refilling, it contains

10.80 units. How much profit will the company make on this container? 4)

A random sample of n=100

observations is drawn from a population with a mean equal to 60

and a standard deviation equal to 20.

a. Find the probability that xx? is less than 56.

b. Find the probability that xx? is greater than 65.

c. Find the probability that falls between 56 and 64.

5)

The average salary for a certain profession is \$69,500.

Assume that the standard deviation of such salaries is

\$25,000. Consider a random sample of 60

people in this profession and let represent the mean salary for the sample.

a.what is ? xx? ?

b.What is ? xx? ? c. Describe the shape of the sampling distribution of xx? 6) Some students paid a private teacher to help them improve their results on a certain mathematical test. These students had

+20 points, with a standard deviation of 65 points. In a random sample of 100 students who

pay a private tutor to help them improve their results,

what is the likelihood that the change in the sample mean score is less than 10 points?

P(xx? &lt;10)=

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