Question

One hundred students took a statistics mid term exam the scores formed a normal distribution with a mean of 84 and a standard deviation of 6 Lucille took the exam but received a 78 on it. What was her approximate percentile tank

Answer 1

The percentile of Lucile is 15%.

Explanation:

As per given data

Mean=μ=84

Standard Deviation=σ=6

Marks of Lucille=X=78

So the percentile for the normal distribution is given as

For this the Z value is calculated as

`z=(X-\mu)/(\sigma)\\z=(78-84)/(6)\\z=(-6)/(6)\\z=-1`

For the Z value of -1, from the Z table the value of P is found as

P(X<78)=P(Z<-1)=0.1587=15.87%

So the percentile of Lucile is 15%.