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 69.3 and a standard deviation of 29.45. (a) What percentage of students taking the test had scores between 60 and 80? (Round your answer to one decimal place.) % (b) At what score was the rate of change of the probability density function for the scores a maximum?

Answer 1

Hello Sir/ Mam

(a) YOUR REQUIRED ANSWER IS 26.57%

80 69.3. P(z P(X 80) P(z _ 29,45

P(X80) P(2< 0.363328) 0.6418 64.18%

60 69.3 P(z P(X60) P(z _ 29,45

P(X60) P(<-0.315789) 0.3761 37.61%

P(60 X<80) 0.6418 0.3761 0.2657 26.57%

(b) YOUR ANSWER IS 39.85

A normal distribution faces the maximum rate pf change at the rising point of inflection. Hence,

a 69.3- 29.45 39.85

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