Question

in a normally distributed population what are the approximate chances- 0.1%, 2.5%, 16%, 50%, 84%, 97.5%, 99%- that a randomly selected value will have a z-score LOWER than the following: a) 0 b) 3.0 c) -1.96 d) -1.0 e) -3.0?

the answers i got where

a) 50% b) 99% c) 2.5% d) 16% e) 0.1%

I got these answers by looking for the values on the z-score table, then finding the percentage by the given decimal.

i want to know if i am correct or not. if i am not please show me how to correctly answer this questiion. thank you!  also if the method for finding z-score HIGHER than the following is a different method.

Answer 1

Solution:

Yes your findings are correct. Also I am giving you some excel formulae for all these questions.

a) Excel formula: =NORMSDIST(0)

Percentage = 0.5 = 50%

b) Excel formula: =NORMSDIST(3)

Percentage = 0.99 = 99%

c) Excel formula: =NORMSDIST(-1.96)

Percentage = 0.025 = 2.5%

d) Excel formula: =NORMSDIST(-1)

Percentage = 0.159 = 16%

e) Excel formula: =NORMSDIST(-3)

Percentage = 0.001 = 0.1%

Also you can find higher than percentages. Just subtract above percentage from 100.

Done