Question

Find the following percentiles for the standard normal distribution. Interpolate where appropriate. (Round your answers to two decimal places.) (a) 81st (b) 19th (c) 76th (d) 24th (e) 11th

Answer 1

Answer:

(a) 81st

=NORM.INV(0.81;0;1)

$0.878$

(b) 19th

=NORM.INV(0.19;0;1)

$-0.878$

(c) 76th

=NORM.INV(0.76;0;1)

$0.706$

(d) 24th

=NORM.INV(0.24;0;1)

$-0.706$

(e) 11th

=NORM.INV(0.11;0;1)

$-1.227$

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Solution to the problem

For this case we can find the percentiles with the Norm.inv function in Excel and we got:

(a) 81st

=NORM.INV(0.81;0;1)

$0.878$

(b) 19th

=NORM.INV(0.19;0;1)

$-0.878$

(c) 76th

=NORM.INV(0.76;0;1)

$0.706$

(d) 24th

=NORM.INV(0.24;0;1)

$-0.706$

(e) 11th

=NORM.INV(0.11;0;1)

$-1.227$