Scores on a 100-point final exam administered to all applied calculus classes at

Question

Scores on a 100-point final exam administered to all applied calculus classes at a large university are normally distributed with a mean of 73.5 and a standard deviation of 26.45.

(a) What percentage of students taking the test had scores between 60 and 80? (Round your answer to one decimal place.)
%

(b) What percentage of students taking the test had scores of at least 90? (Round your answer to one decimal place.)
%

(c) What percentage of students taking the test had scores that were more than one standard deviation away from the mean? (Round your answer to one decimal place.)
%

(d) At what score was the rate of change of the probability density function for the scores a maximum?

Explanation / Answer

a) From information given, Xbar=73.5, s=26.45, Obtain z scores corresponding to Xi=60 and 80.

z1=(60-73.5)/26.45=-0.51 and z2=(80-73.5)/26.45=0.25

Find areas corresponding to respective z scores and add the areas to find required probability.

Ans: (0.1950+0.0987)=0.2937

b) P(X>=90)=P(z>=90)=P[(90-73.5)/26.45]=P(Z=0.62)=0.2676. ans:26.76%.

c) Around 34.13% students taking the test had scores that were more than 1 sd from mean.

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.