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Each year the admissions committee at a top business school receives a large number of applications for admission to the MBA program and they have to decide on the number of offers to make. Since some of the admitted students may decide to pursue other opportunities, the committee typically admits more students than the ideal class size of 720 students. You were asked to help the admission committee estimate the appropriate number of people who should be offered admission. It is estimated that in the coming year the number of people who will not accept the admission is normally distributed with mean 50 and standard deviation 21. Suppose for now that the school does not maintain a waiting list, that is, all students arc accepted or rejected. a. Suppose 750 students are admitted. What is the probability that the class size will be at least 720 students'

Sagot :

Answer:

0.1711 = 17.11% probability that the class size will be at least 720 students

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

In this question:

Our random variable X is the number of students not taking admission, which has mean [tex]\mu = 50[/tex] and standard deviation [tex]\sigma = 21[/tex]

a. Suppose 750 students are admitted. What is the probability that the class size will be at least 720 students?

30 or less students do not take admission, which means that this is the pvalue of Z when X = 30.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{30 - 50}{21}[/tex]

[tex]Z = -0.95[/tex]

[tex]Z = -0.95[/tex] has a pvalue of -0.1711

0.1711 = 17.11% probability that the class size will be at least 720 students

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