Harry, Jason, and Sarah are taking the GMAT exam, which is required by most applicants for admission to graduate schools of business. The three friends aim to get admission to three different business schools.

- Harry can get admission if he scores above 650 on the GMAT.
- Jason can get admission if he scores above 630.
- Sarah can get admission if she scores 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 Harry, Jason, and Sarah will get 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 all be accepted into their desired schools is;P(Harry, Jason, Sarah) = P(Harry) * P(Jason) * P(Sarah) = 0.1949 * 0.2413 * 0.1492 = 0.007 Possible answer: 0.007 (or 0.7%)

The solution to the question is given below; The mean score of the GMAT exam is μ = 550 and the standard deviation is σ = 115.There are three friends - Harry, Jason, and Sarah - who want to be admitted to business schools. Harry requires a score of 650 or above, while Jason requires a score of 630 or higher and Sarah requires a score of 670 or above. Because the admission procedure is independent for each of the friends, the joint probability can be calculated using the multiplication rule.

The probabilities that Harry, Jason, and Sarah will achieve the desired scores are calculated separately using the z-score equation, which is as follows;For Harry:Z = (650 - 550) / 115 = 0.87 Probability of Harry getting admitted = P(z > 0.87) = 0.1949 (using z-table)For Jason:Z = (630 - 550) / 115 = 0.7 Probability of Jason getting admitted = P(z > 0.7) = 0.2413 (using z-table)For Sarah:Z = (670 - 550) / 115 = 1.04 Probability of Sarah getting admitted = P(z > 1.04) = 0.1492 (using z-table)The probability that Harry, Jason, and Sarah will all be accepted into their desired schools is;P(Harry, Jason, Sarah) = P(Harry) * P(Jason) * P(Sarah) = 0.1949 * 0.2413 * 0.1492 = 0.007 Possible answer: 0.007 (or 0.7%)

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