In a recent year, the MCAT total scores were normally distributed, with a mean of 500 and a standard deviation of 10.6.  Find the probability that a randomly selected medical student who took the MCAT has a total score that is:a.  less than 489b.  between 495 and 507c.  more than 522

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Asked Dec 3, 2019
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In a recent year, the MCAT total scores were normally distributed, with a mean of 500 and a standard deviation of 10.6.  Find the probability that a randomly selected medical student who took the MCAT has a total score that is:

a.  less than 489

b.  between 495 and 507

c.  more than 522

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Expert Answer

Step 1

Consider,

Let X be a random variable that represents the total score which is normally distributed that is,

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X-N(μ= 500, σ = 10.6)

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Step 2

(a)

The probability that randomly selected students have score less than 489:

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X-и 489-500 х-и P(x < 489) P 10.6 P(Z<-1.0377) 0.149

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Step 3

(b)

The probability that randomly selected stud...

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495-500 X-u 507-500 P(495 < X <507)= P| 10.6 10.6 - P(-0.471< Z< 0.660) -P(0.660)-P(-0.471) 0.426 495 507

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