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

Question

Quizplus · Accepted Answer

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.

A University in Your Region Estimates That Graduating Average of High