Data are drawn from a bell-shaped distribution with a mean of 90 and a standard

ID: 3321636 • Letter: D

Question

Data are drawn from a bell-shaped distribution with a mean of 90 and a standard deviation of 5.

Approximately what percentage of the observations fall between 80 and 100? (Round your answer to the nearest whole percent.)

Approximately what percentage of the observations fall between 75 and 105? (Round your answer to the nearest whole percent.)

Approximately what percentage of the observations are less than 85? (Round your answer to 1 decimal place.)

Data are drawn from a bell-shaped distribution with a mean of 90 and a standard deviation of 5.

mean is 90 and s is 5

z is given as (x-mean)/s

a) P(80<x<100)=P((80-90)/5<z<(100-90)/5)=P(-2<z<2)=2*P(z<2)-1 , from normal table we get 2*0.9772-1=0.9544

b) P(75<x<105)=P((75-90)/5<z<(105-90)/5)=P(-3<z<3)=2*P(z<3)-1, from normal table we get 2*0.9987-1=0.9974

c) P(x<85)=P(z<(85-90)/5)=P(z<-1) or 1-P(z<1) or 1-0.8413=0.1587

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