In a recent year, the scores for the reading proton of a test were normally dist

Question

In a recent year, the scores for the reading proton of a test were normally distributed. with a mean of 23.2 and a standard deviation of 6.1. Complete parts (a) through (d) below Find the probability that a randomly selected high school student who took the reading portion of the test has a score that is less than 21. the probability of a student scoring loss than 21 it 3594 (Round to four decimal places as needed.) Find the probability that a randomly selected high school student who took the reading portion of the test has a score that is between 19.5 and 26.9. the probability of a student scoring between 19.5 and 26.9 is (Round to four decimal places as needed.)

Explanation / Answer

here we calculate standard normal variate z=(x-mean)/sd

(1) for x=21, z=(21-23.2)/6.1=-0.3607

P(x<21)=P(z<-0.3067)=0.3592 ( using ms-excel command =NORMSDIST(-0.3607)

(2)P(19.5<x<26.9)=P(-0.6066<z<6066)=P(z<0.6066)-P(z<-0.6066)=0.7279-0.2721=0.4558

for x=19.5, z=(19.5-23.2)/6.1=-0.6066

for x=26.9, z=(26.9-23.2)/6.1=0.6066

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