The score on an exam from a certain statistics class, X, is normally distributed

Question

The score on an exam from a certain statistics class, X, is normally distributed with mu = 77.2 and sigma = 10. A score can thus take on any value on the continuum. (In real life, scores are often treated as if they were continuous values but are actually discrete in most cases.) Write the event "a score less than 62.2" in terms of X: Find the probability of this event: Find the probability that a randomly chosen score is greater than 87.2: Find the probability that a randomly chosen score is between 62.2 and 87.2:

Explanation / Answer

Here mu=77.2 and sd=10

1. The event less than 62.2 is X<62.2

2. P(X<62.2)=P(z<62.2-77.2/10)=P(z<-1.5)=0.0668

3. P(X>87.2) converting this to z we get P(z>87.2-77.2/10)=P(z>1)=1-P(z<=1)=0.1587

4. P(62.2<x<87.2) as we have converted both above inot z we will use directly the value P(-1.5<z<1)=P(z<1)-P(z<=-1.5)=0.8413-0.0668=0.7745

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