Random variable Z follows standard normal distribution, random variable X is normal distribution with $N (7.5, 10^2)$ where $P (Z> 1.960)=0.025$ and $P (Z> 1.645) = 0.05$ I`m not sure especially for a and b
i need to find:
a. $P(|z|>1.96)$
by definition of absolute function, $P(z \ge 1.96 or p \le -1.96) =2 *0.025=0.05$
b.$P(x>a)=0.025$
$P(\frac{x-7.5}{10}>\frac{a-7.5}{10})=0.025$
we know that z for 0.025 is 1.96
therefore, $1.96= \frac{a-7.5}{10}$
$19.6+7.5=a$
$a=27.1$
c.$P(x<23.95)$ = $1- p(\frac{x-7.5}{10} \ge \frac{23.95-7.5}{10})$=$ 1- 0.05=0.95$
this looks simple, but i dont want to miss important step