Can someone help me answer this question? Be as detailed on how to answer it as possible because I don't get it at all...

Question

A random variable r is normally distributed with a mean of 7 and a standard deviation of 1.5. Find the vaule of w so hat P(8.8<r<w)=.0800

Answer 1

Prob( 8.8 < r < w ) = 0.08

Prob ( r < w) - Prob( r < 8.8) = 0.08

Prob( r<w) = 0.08 + Prob(r < 8.8)

Prob(r<w) = 0.08 + Prob ( z < (8.8-7)/1.5)

= 0.08 + Prob( z < 1.2)

= 0.08 + 0.88493

= 0.96493

Per the table, Prob (z < 1.811006) = 0.96493

z = (w- mean)/stddev

1.811006 = (w- 7)/1.5

w = 1.811006*1.5+7 = 9.716509