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 more than 20 suitcases?
A)0.1056
B)0.3944
C)0.4040
D)0.8944

Question

Quizplus · Accepted Answer

To find the probability of losing more than 20 suitcases, we use the Z-score formula: $Z = \frac{X - \mu}{\sigma}$, where $X = 20$, $\mu = 15.5$, and $\sigma = 3.6$. This gives $Z = \frac{20 - 15.5}{3.6} = 1.25$. Looking up 1.25 in the Z-table gives the probability of being below 1.25, so we subtract this from 1 to find the probability of being above 1.25, which is approximately 0.1056.

An Airline Knows from Experience That the Distribution of the Number