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Please help me heres the question: Ms. Zanetti receives text messages throughout her work day from her daughter’s day care provider. The possible number of text messages that she receives in a given day and the probabilities are given in the table.PLEASE SEND ANSWER ASAP

User Pzearfoss
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2 Answers

18 votes
18 votes

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)

User Bart Beyers
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3.1k points
19 votes
19 votes

Answer:

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Step-by-step explanation:

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User OzgurG
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3.0k points
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