Final answer:
Text message users receive or send an average of 41.5 text messages per day. a. The number of text messages a user receives or sends per hour is approximately 1.7292. b. The probability that a user receives or sends two messages per hour is approximately 0.2165. c. The probability that a user receives or sends more than two messages per hour can be found by subtracting the cumulative probability of receiving or sending 0, 1, and 2 text messages per hour from 1.
Step-by-step explanation:
a. How many text messages does a text message user receive or send per hour?
To find the number of text messages a user receives or sends per hour, we need to divide the average number of text messages per day by 24 (the number of hours in a day). In this case, the average number of text messages per day is 41.5, so:
Number of text messages per hour = 41.5 / 24 ≈ 1.7292
b. What is the probability that a text message user receives or sends two messages per hour?
To find the probability of a user receiving or sending two text messages per hour, we need to use the average number of text messages per hour (1.7292) in a Poisson distribution. The formula for the Poisson distribution is:
P(x; λ) = (e^(-λ) * λ^x) / x!
Using λ = 1.7292 and x = 2, we can calculate the probability:
P(2; 1.7292) ≈ 0.2165
c. What is the probability that a text message user receives or sends more than two messages per hour?
To find the probability of a user receiving or sending more than two text messages per hour, we need to calculate the cumulative probability of receiving or sending 0, 1, and 2 text messages per hour and subtract it from 1.
P(x > 2; 1.7292) = 1 - P(x ≤ 2; 1.7292)