On the average, a student takes 102 words/minute midway through an advanced cour

Question

On the average, a student takes 102 words/minute midway through an advanced court reporting course at the American Institute of Court Reporting. Assuming that the dictation speeds of the students are normally distributed and that the standard deviation is 17 words/minute, find the probability that a student randomly selected from the course can make dictation at the following speeds. (Give your answers to four decimal places.) (a) more than 119 words/minute (b) between 119 and 136 words/minute (c) less than 68 words/minute

Explanation / Answer

Let, X be the random variable denoting the speed of the student.

Then, X follows Normal(102,172) distribution

If we take Y=(X-102)/17 ,

then Y is a standard normal random variable.

So, using table for cumulative probability for standard normal distribution, we get:

a) Ans= P(X>119)=P(Y>1)=0.1587

b)Ans= P(119<X<136) =P(1<Y<2)=0.1359

c)Ans= P(X<68) =P(Y<-2) =0.0228

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