Question

Suppose 400 students take an exam and the distribution of their scores can be treated as normal. Find the number of scores falling into each of the following ranges:

(a)   Within 1 standard deviation of the mean.

(b)  Within 2 standard deviations of the mean.

Answer 1

P(z<Z) table :

a.

from the table above we see that data within 1 SD

P(-1 < z < 1) = P(z<1) - P(z<-1)

= 0.8413 - 0.1587

= 0.6826

number of scores within 1 SD :

= n*P(-1<z<1)

= 400*0.6826

= 273.04

b.

from the table above we see that data within 2 SD

P(-2 < z < 2) = P(z<2) - P(z<-2)

= 0.9772 - 0.0228

= 0.9544

number of scores within 2 SD :

= n*P(-2<z<2)

= 400* 0.9544

= 381.76

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