Question

Help me please, algebra 1 statistics question.

Answer 1

Scores on a statewide standardized test are normally distributed with a mean of 12.89 and a standard deviation of 1.95. Certificates are given to students whose scores are in the top 2% of those who took the test. This means that they scored better than 98% of the other test takers. Marcus received his score of 13.7 on the exam and is wondering why he didn’t receive a certificate. Show all work to determine whether Marcus’ score was high enough to earn a certificate. Write a letter to Marcus explaining whether or not he will be receiving a certificate. Include a brief summary of your statistical analysis in your letter.

Answer 2

Any help is appreciated.

Answer 3

In school one is usually taught to calculate a so-called z-score. Does this mean something to you? To obtain it one subtracts the population mean for the test from the individual's score on a test and then divides by the population standard deviation, thus:

( 13.7 - 12.89 ) / 1.95 = 0.415

Then Marcus' standardised score or z-score is 0.415. This will have come from a normal distribution with mean 0 and standard deviation 1. This transformation is made because the percentiles for this distribution are widely tabulated. For example, most of these tables will indicate how big a z-score must be so that it is greater than or equal to, 95% of all of the values in the entire population. When I look up 0.415 I find that only about 67.4% of the population scored less than this.

If I look up 96% in a table I find that this corresponds to a z-score of about 1.75. If I multiply by 1.95, then add 12.89 I calculate 16.3, which is what Marcus would need if the minimum standard were the top 4%.

I leave it to you to work out the number for the required 2% on these same lines.

Answer 4

I'm still confused...can someone help clear things up?