A class of 250 students took a test. Suppose their scores were normally distribu

Question

A class of 250 students took a test. Suppose their scores were normally distributed with a mean score of 70 and a standard deviation of 10. Answer the following questions.

(a) WHAT STANDARD SCORE (z-score) "cuts off" an area in the right tail of 0.05 = 5%? That is, for what value of z is there a 5% probability of a score being greater than z? You will need to use Table B1. Remember that the table shows the area from 0 to z. Also, you will need to interpolate between two values in the table. Report your answer to 3 decimal places.


(b) Sally is one of the students. What is the minimum ("cutoff") RAW SCORE must she get in order to be in the top 5% of the class on this test? Round to the nearest whole number.

Explanation / Answer

a) for right tail value of 0.05 ; critical value of z =1.645

b)minimum score required =mean +z*std deviation =70+1.645*10 =86

(please try 87 if above does not work due to rounding on upside)

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