# An examination is marked out of 100. It is taken bby a large number of candidates. The mean for all candidates is 72.1 and the standard deviation is 15.2. Give a reason why a normal distribution...

An examination is marked out of 100. It is taken bby a large number of candidates. The mean for all candidates is 72.1 and the standard deviation is 15.2. Give a reason why a normal distribution with this mean and standard distribution, would not give a good approximation to the distribution of marks.

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### 1 Answer

Standard normal random variable

`Z=(X-mu)/sigma`

`We` have given `mu=72.1 and sigma=15.2`

Thus

`Z=(100-72.1)/15.2=1.84`

`Z=(0-72.1)/15.2=-4.74`

Thus

`P(0<=X<=100)=.967`

Thus

`P(X<0)+P(X>100)=1-.967=.033`

ie. 3.3% which is ,non negligible probabilty 3.3 % significant

Thus normal is non fit for this marks distribution.