Statistics

Question

Normal distribution with mean 73 & standard deviation 8; find:

Formula: Z = (X - u)/ o    { u=mean; o=standard dev.

(i) prob. of getting  91 OR less   scores.
Assumed to be: P (X < = 91)

(ii) prob. of getting  less than 91  scores.
Assumed to be: P (X < 91)

So, calculations & answers of (i) & (ii) should be different? Right?

Please calculate by applying the formula in detailed steps. TKS!

? · Accepted Answer

The value of (i) and (ii) should be the same as P(X = a) = 0 when x follows a continuous distribution.

Asnwer:  (i) and (ii) 0.987776
 
(i) P(X <= 91)

= P[(X - 73)/8 <= (91 - 73)/8]

= P(Z <= 2.25)

= 0.987776

(ii) Similar as (i) but replace 'less than or equal to' by 'less than'