A sample of distributed is normally distributed with a mean equal to 27 and a va

Question

A sample of distributed is normally distributed with a mean equal to 27 and a variance equal to 25 scores El Part (a) What percentage of scores are between 22 and 32? (Round your answer to two decimal places.) 10 X El Part (b) What raw score is the cutoff for the top 10% of scores? (Round your answer to one decimal place. El Part (c) What is the proportion below 20? (Round your answer to four decimal places.) El Part (d) What is the probability of a score less than 34? (Round your answer to four decimal places.)

Explanation / Answer

Mean is 27 and standard deviation is sqaure root of variance= sqrt(25)=5

a. P(22<x<32)=P((22-27)/5<Z<(32-27)/5)=(-1<Z<1)=P(Z<1)-(1-P(Z<1))=2P(Z<1)-1. From the normal distribution table, it is given by 2*0.8413-1 =68.26%

b. P(x<X)=0.9 (we are looking at the topmost value at 90%)

from normal table, z=1.28 for p=0.9

thus (x-27)/5=1.28 or x=1.28*5+27=33.4

c. P(x<20)=P(z<(20-27)/5)=P(z<-1.4)=1-P(z<1.4)=1-0.9192=0.0808

d. P(x<34)=P(z<(34-27)/5)=P(z<1.4)=0.9192

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