Question

4. The time that it takes a person to complete a survey is normally distributed with a mean of 18 minutes and a standard deviation of 3.5 minutes. (a)  Find the 45’th percentile.

Answer 1

We have given:

Mean = 18 and Standard deviation = 3.5

We have asked to find the 45th percentile, that is Raw score (x).

We know that-

Raw score (x) = Zc * +

Therefore, 45th percentile = Z0.45 * (3.5) + 18

From the Z table we get - Z0.45 = -0.1257

Hence 45th percentile = [( - 0.1257) * (3.5)] + 18

= (-0.4398) + 18

= 17.5602

In excel you can directly use the command =NORMINV(0.45,18,3.5)

= 17.5602

45th percentile = 17.5602 (Rounded to the 4 decimal)

Hope this will help you. Thank you :)