Question

6. Number of passengers who arrive at the platform in an Amtrack train station for the 2 pm train on a Saturday is a random variable with a mean of 180 and a standard deviation of 20. a) With what probability can we assert that there will be between 120 and 240 passengers

Answer 1

Answer:

99.7%

Step-by-step explanation:

Mean number of passengers (μ) = 180 passengers

Standard deviation (σ) = 20 passengers

The number of standard deviation from the mean for the lower and upper bounds of the 120 to 240 passengers intervals are:

$L = \frac{180-120}{20} =3\\U = \frac{240-180}{20} =3$

Therefore, all of the data is within 3 standard deviations from the mean. According to the empirical rule, 99.7% of the data is within 3 standard deviations from the mean. Therefore, we can assert with a 99.7% probability  that there will be between 120 and 240 passengers.