Riders' Excitement: Approximate Number of Subway Trips Last January

How many subway riders took between 30 and 43 trips last January?

For a population of 800,000 subway riders, the numbers of subway trips taken per rider last January are approximately normally distributed with a mean of 56 trips and a standard deviation of 13 trips.

Answer:

Approximately, how many of the riders took between 30 and 43 trips last January?

To find out the approximate number of subway riders who took between 30 and 43 trips last January, we can use the concept of the normal distribution curve. Given that the mean number of trips taken was 56 and the standard deviation was 13, we can calculate the z-scores for 30 and 43.

First, we calculate the z-score for 30 trips:
z = (x - mean) / standard deviation
z = (30 - 56) / 13 ≈ -2

Next, we calculate the z-score for 43 trips:
z = (x - mean) / standard deviation
z = (43 - 56) / 13 ≈ -1

By referring to the z-score table, we can find that the area to the left of z = -2 is approximately 0.0228 and the area to the left of z = -1 is approximately 0.1587. To find the approximate number of riders who took between 30 and 43 trips, we need to calculate the difference between these two probabilities.

Probability between 30 and 43 trips ≈ Probability(z < -1) - Probability(z < -2)
≈ 0.1587 - 0.0228
≈ 0.1359

Finally, we can calculate the approximate number of riders who took between 30 and 43 trips last January by multiplying this probability by the total rider population:
Riders ≈ Probability between 30 and 43 trips * Total riders
≈ 0.1359 * 800,000
≈ 108,720

Therefore, approximately 108,720 subway riders took between 30 and 43 trips last January. It's amazing to see how the data can help us understand the behavior of the subway riders in New York City!