Question

provide an appropriate response. use the standard normal table to find the 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 μ = 15.5 and σ = 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. 0.4040
d. 0.1056

Explanation:

Step1: Calculate 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 probability from table

Look up the z - score of 1.25 in the standard normal table. The value corresponding to $z = 1.25$ in the standard - normal table is 0.8944. This represents the probability that $Z<1.25$, which is the probability that the airline will lose less than 20 suitcases.

Answer:

A. 0.8944