# [SOLVED]normal distribution to standard distribution

#### karush

##### Well-known member
this is an image of the given problem
View attachment 1137
so for (a) (i) I used $\frac{x-\mu}{\sigma}=z \frac{0.70-0.76}{0.06}=-1 = a$ and $\frac{0.79-0.76}{0.06}=.5 = b$

(ii) $P(.70<X)$ z-table for $-1$ is $0.3413$ so $0.3413 + .500 = 0.8413$

$P(.70<X<.79)$ z-table for $.5$ is $0.1915$ so $0.3413+0.1915=0.5328$

will get to (b) later
hope so far is

#### MarkFL

Staff member
Looks good so far!

#### karush

##### Well-known member
(b) (i)
View attachment 1139

(ii) z-table for $3\% \approx -1.88$

so $\frac{c-0.76}{0.06}=-1.88$ thus $c\approx 0.65 s$

my shaky attempt at this anyway