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?
A)0.8944
B)0.3944
C)0.1056
D)0.4040

Question

Quizplus · Accepted Answer

To find the probability of losing less than 20 suitcases, we use the Z-score formula: $Z = \frac{X - \mu}{\sigma}$, where $X$ is 20, $\mu$ is 15.5, and $\sigma$ is 3.6. Calculating the Z-score gives us $Z = \frac{20 - 15.5}{3.6} = 1.25$. Looking up 1.25 in the Z-table gives us a probability of 0.8944, indicating the probability of losing less than 20 suitcases is 0.8944.

An Airline Knows from Experience That the Distribution of the Number