Scores on a Recent National Statistics Exam Were Normally Distributed

question 166

Short Answer

Scores on a recent national statistics exam were normally distributed with a mean of 80 and a standard deviation of 6.
a.What is the probability that a randomly selected exam will have a score of at least 71?
b.What percentage of exams will have scores between 89 and 92?
c.If the top 2.5% of test scores receive merit awards, what is the lowest score eligible for an award?
d.If there were 334 exams with scores of at least 89, how many students took the exam?

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Definitions:

Bank Capital

The funds that are held by a bank that are used as a cushion against potential losses, ensuring the bank's stability and financial health.

Invested Capital

The total amount of money that shareholders and debt holders have invested in a company for long-term use.

Gross Assets

The total asset value on a company's balance sheet before deducting any liabilities or depreciation.

Capital Asset Ratio

This ratio measures a bank's financial strength by comparing its capital to its assets, assessing the bank's ability to withstand losses.