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

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)= 