Question

1. (02.04 mc) the length of a phone conversation is normally distributed with a mean of 4 minutes and a standard deviation of.6 minutes. what is the probability that a conversation lasts longer than 5 minutes? (5 points) 0.04746 0.45254 0.54746 0.95254

Explanation:

Step1: Calculate z-score

The z-score formula is $z=\frac{x-\mu}{\sigma}$, where $x=5$, $\mu=4$, $\sigma=0.6$.
$z=\frac{5-4}{0.6}=\frac{1}{0.6}\approx1.67$

Step2: Find upper tail probability

We need $P(X>5)=P(Z>1.67)$. Using standard normal table, $P(Z\leq1.67)=0.9525$.
$P(Z>1.67)=1-0.9525=0.0475$, which rounds to 0.0476.

Answer:

0.04746