Airline Weekly Suitcase Loss Prediction

What percentage of weeks does the airline will lose less than 20 suitcases?

Based on the data provided, how can we calculate the percentage of weeks when the airline loses less than 20 suitcases?

Calculation of Percentage

To find the percentage of weeks when the airline loses less than 20 suitcases, we need to calculate the cumulative probability up to the value of 20 from a normal distribution with a mean (μ) of 15.5 and a standard deviation (σ) of 3.6.

An airline predicts the number of lost suitcases each week on a certain route to be approximately normal with a mean (μ) of 15.5 and a standard deviation (σ) of 3.6. With this information, we can determine the likelihood of losing less than 20 suitcases in a week.

Step 1: Standardize the value of 20 using the z-score formula:

z = (x - μ) / σ

where x is the value (20), μ is the mean (15.5), and σ is the standard deviation (3.6).

z = (20 - 15.5) / 3.6 ≈ 1.25

Step 2: Find the cumulative probability (P) corresponding to the calculated z-score. This can be done using a standard normal distribution table or a calculator.

Using a standard normal distribution table or a calculator, we find that the cumulative probability corresponding to a z-score of 1.25 is approximately 0.8944.

Step 3: Convert the cumulative probability to a percentage by multiplying by 100:

Percentage = P * 100 = 0.8944 * 100 ≈ 89.44%

Therefore, approximately 89.44% of weeks does the airline lose less than 20 suitcases on the given route. This is a positive outlook for the airline, indicating that the majority of weeks are likely to experience a lower number of lost suitcases.