Harry, Jason, and Sarah are taking the GMAT quiz, which is required by most applicants for admission to graduate schools of business. They want to gain admission to three different business schools, each requiring different GMAT scores:

- Harry needs a score above 650.
- Jason needs a score above 630.
- Sarah needs a score above 670.

Scores on the GMAT are roughly normally distributed with a mean of 550 and a standard deviation of 115.

What is the probability that all three will gain admission to their desired schools, given that they study independently and the admissions are independent of one another?

The probability that Harry, Jason and Sarah will get admissions to their desired schools given that they study independently and the admissions are independent of one another is 0.007 or 0.7%.

Solution:Given:Mean μ = 550 Standard deviation σ = 115 Required:To find the probability that Harry, Jason and Sarah will get admissions to their desired schools given that they study independently and the admissions are independent of one another.Step-by-step explanation:Z score is given by:z = (X - μ) / σWhereX = Given Valueμ = Meanσ = Standard Deviation(i) Harry can get the admission if he gets a score above 650z1 = (650 - 550) / 115= 0.87(ii) Jason can get the admission if he gets above 630z2 = (630 - 550) / 115= 0.70(iii) Sarah can get the admission if she gets above 670z3 = (670 - 550) / 115= 1.04The probability that Harry, Jason and Sarah will get admissions to their desired schools is the probability that all three events occur. As these events are independent, we multiply their probabilities.

P(Harry getting admission) = P(Z > 0.87) = 0.1949 P (Jason getting admission) = P(Z > 0.70) = 0.2417 P (Sarah getting admission) = P(Z > 1.04) = 0.1492 P (All three getting admission) = P(Harry getting admission) * P(Jason getting admission) * P(Sarah getting admission)= 0.1949 * 0.2417 * 0.1492= 0.00719≈ 0.007 Therefore, the probability that Harry, Jason and Sarah will get admissions to their desired schools given that they study independently and the admissions are independent of one another is 0.007 or 0.7%.

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