Scores on an examination are assumed to be normally distributed with mean 78 and variance 36.
a What is the probability that a person taking the examination scores higher than 72?
b Suppose that students scoring in the top 10% of this distribution are to receive an A grade. What is the minimum score a student must achieve to earn an A grade?
c What must be the cutoff point for passing the examination if the examiner wants only the top 28.1% of all scores to be passing?
d Approximately what proportion of students have scores 5 or more points above the score that cuts off the lowest 25%?
e Applet Exercise Answer parts (a)–(d), using the applet Normal Tail Areas and Quantiles.
f If it is known that a student’s score exceeds 72, what is the probability that his or her score exceeds 84?
Step 1: Goal
To find the probability that a person taking the examination scores higher than 72.