A university in your region estimates that graduating average of high school students who apply for admission to a particular university program can be described by a Normal model with a mean of 82% and a standard deviation of 5%.The staff in admissions opens the applications at random looking for 10 applicants with averages above 85%.How many applications do you think the staff will need to open?

A) About 36 applications
B) About 21 applications
C) About 10 applications
D) About 28 applications
E) About 14 applications

To find the number of applications needed, first calculate the probability of a student having an average above 85%. Using the Z-score formula: Z = (X - μ) / σ, where X is 85, μ is 82, and σ is 5, we get Z = (85 - 82) / 5 = 0.6. Looking up 0.6 on the Z-table gives a probability of about 0.7257 to the left, so the probability to the right (above 85%) is 1 - 0.7257 = 0.2743. To find one student with an average above 85%, we expect 1 / 0.2743 ≈ 3.64 applications. For 10 students, multiply by 10, giving approximately 36.4 applications, which rounds to about 36 applications.