Question

In a standard normal distribution, what is the probability of randomly selecting a value between -2.555 and -0.745? Round to four decimal places.

Answer 1

Task. In a standard normal distribution, what is the probability of randomly selecting a value between $-2.555$ and $-0.745$? Round to four decimal places.

Solution. Let $X$ be the random variable having standard normal distribution. Then the values of its distribution function

$F(t)=P(X<t)$

can usually be found in any book in probability theory.

We should compute the probability

$P(-2.555\leq X\leq-0.745)=F(-0.745)-F(-2.555)\approx 0.228136-0.005309\approx 0.2228.$