Question

find the indicated probability. an airline knows from experience that the distribution of the number of suitcases that get lost each week on a certain route is approximately normal with $mu = 15.5$ and $sigma = 3.6$. what is the probability that during a given week the airline will lose less than 20 suitcases? 0.3944 0.1056 0.8944 0.4040

Explanation:

Step1: Calculate the z - score

The formula for the z - score is $z=\frac{x-\mu}{\sigma}$, where $x = 20$, $\mu=15.5$, and $\sigma = 3.6$.
$z=\frac{20 - 15.5}{3.6}=\frac{4.5}{3.6}=1.25$

Step2: Find the probability from the standard normal table

We want to find $P(X < 20)$, which is equivalent to $P(Z<1.25)$ when $X$ is normally distributed with mean $\mu$ and standard deviation $\sigma$ and $Z$ is the standard normal variable. Looking up the value of $P(Z < 1.25)$ in the standard - normal table, we get $P(Z<1.25)=0.8944$.

Answer:

C. 0.8944