A large group ofstudents took a statistics test. The mean score, from the scale

Question

A large group ofstudents took a statistics test. The mean score, from the scale of 100, was 70 with a standard deviation of 8.5. The test scores have a bell-shaped distribution. 24 Students who scored less than 55 failed the test. What fraction of students failed the test? 0.0392 0.0495 0.0559 0.0643 25 Ifthe minimum score for the letter grade B is 76, what fraction of students received a grade of B or higher. 0.2877 0.2776 0.2578 0.2389 26 Ifthe range of scores for a C is 65-75, what fraction of students received a C? 0.5034 0.4972 0.4844 0.4448 27 what should the minimum score be set at so that a grade ofA is given to the top 5% oftest scores? (Round your answer to the nearest integer.) 84 86 87 90

Explanation / Answer

mean is 70 and s is 8.5

a) P(x<55)=P(z<(55-70)/8.5)=P(z<-1.76) or 1-P(z<1.76) , from normal distribution table we get 1-0.9608 =0.0392 (A)

b) P(x>76)=P(z>(76-70)/8.5)=P(z>0.71)=1-P(z<0.71)=1-1-0.7611=0.2389 (D)

c) P(65<x<75)=P((65-70)/8.5<z<(75-70)/8.5)=P(-0.59 <z<0.59) or 2*P(z<0.59)-1 =2*0.7224-1=0.4448

d) for top 5% we need to look at the value that is at 95% from left of curve: thus z for this is given as 1.65

answer is 70+1.65*8.5=84.025 or option A

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