Question

For a daily airline flight between two cities, the number of pieces of checked luggage has a mean of 380 and a standard deviation of 20. On what percent of the flights would you expect from 340 to 420 pieces of checked luggage?

Answer 1

It would depend on the distribution of the random variable for checked luggage.

If we assume a normal distribution, then you must find the probability that the variable, call it \(X\), falls between 340 and 420:
\[P\left(340<X<420\right)=P\left(\frac{340-380}{20}<\frac{X-380}{20}<\frac{420-380}{20}\right)=P\left(-2<Z<2\right)\]
Where \(Z=\dfrac{X-380}{20}\) is the transformation from a normal to standard normal random variable.

Refer to a chart for the probability.