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 78 and standard deviation 8.1

a. A particular employer requires job candidates to score at least 83 on the dexterity test. Approximately what percentage of the test scores during the past year exceeded 83?

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% were higher). What was the candidate's score?

Click here to view a table of areas under the standardized normal curve.

a. Approximately --- % of the test scores during the past year exceeded 83

(Round to one decimal place as needed.)

b. The candidate's score was ----

(Round to the nearest whole number as needed.)

2)A business journal investigation of the performance and timing of corporate acquisitions discovered that in a random sample of 2,788 firms ,789 announced one or more acquisitions during the year 2000. Does the sample provide sufficient evidence to indicate that the true percentage of all firms that announced one or more acquisitions during the year 2000 is less than 31%? Use alpha 0.10 to make your decision.

-What are the hypotheses for this test?

-What is the rejection region? Select the correct choice below and fill in the answer box(es) to complete your choice.

(Round to two decimal places as needed.)

-Calculate the value of the z-statistic for this test.

-What is the conclusion of the test?