he scores of students on the ACT (American College Testing)college entrance examination in a recent year had the normaldistribution with mean μ = 18 and standard deviation σ = 6. 100students are randomly selected from all who took the test.
a. What is the probability that the mean score for the100 students is between 17 and 19 (including 17 and 19)?
b. A student is eligible for an honor program ifhis/her score is higher than 25. Find an approximation to theprobability that at least 15 students of the 100 students areeligible for the honor program.
c. If the sample size is 4 (rather than 100), what isthe probability that more than 50% (not include 50%) students areeligible for the honor program?
