Question

If you select a random z-score from the normal distribution, what is the probability that you will get a value greater than -2.5? Put differently, P(z>2.5) = ? (Answer to 3 digits after the decimal.)

(ANSWER ISNT .006) for ^

What critical value of z will give you an answer of exactly 0.01 to the previous question? (Answer to 2 digits after the decimal.)

Answer 1

Z= -2.5

P(Z > -2.5 ) = 1- P( Z < -2.5) = 1- 0.00621= 0.99379 = 0.994

( To find probability we use =NORMSDIST(z) in excel this will gives you less than probability total area under the curve is 1

so subtract from 1 . which gives 0.994)

What critical value of z will give you an answer of exactly 0.01 to the previous question? (Answer to 2 digits after the decimal.)

Alpha = 0.01

For exact =0.01 it gives us 0

In continuous distribution for exact number critical value is 0

Less than Alpha = Area=0.01 The critical value is

Z = -2.33

For greater than 0.01( Area =1-0.01=0.99) the critical value is

Z=2.33       ( Excel command = NORMSINV( Area)

For two tailed critcal value 0.01 ( 1 - (0.01/2) =0.995)

Z=2.58