Need assistance on part B and part C. I have no idea how to do it, need indept e

Question

Need assistance on part B and part C. I have no idea how to do it, need indept explaination. Thank you so much! Will give thumbs up!

Problem #1-The number of calls received per hour by a customer service call center has an average rate of 80 calls per hour. To receive credit you must show your calculations. 1. A. Find the probability that at most 4 calls are received in a three-minute interval. a. What is the random variable and its distribution? Circle the correct answer i. The random variable, X - number of calls received in a three-minute interval, ii. The random variable, X-the time until the fourth call is received, ii. The random variable, X - number of calls received per minute, X~Poi(4/3) X~Poi(4) X-Gamma(4,3/4) iv. The random variable, X the time until the fourth call is received, X Gamma(4,4) Compute the probability. Perform your calculations below and then circle the correct (closest) answer b. i 0.6290 0.5670 iii. 0.0190 iv. 0.4330 Calculate the variance of the random variable from part i. Perform vour calculations below and then circle the correct answer. i. 4/3 c. iv. 64

Explanation / Answer

b)
By poisson distribution,

P(x, m)= e^-m * m^x / x!

Here, m = 80 calls per hour but we need 4 calls in 3 minute interval
so, m = 80 * 3 / 60 = 4

P(X < 4) = P(x= 0) + p(x =1) + P(x = 3) + P(x = 4)

= e^-4 * 4^0 / 0! + e^-4 * 4^1 / 1! +e^-4 * 4^2 / 2! +e^-4 * 4^3 / 3!
= 0.4330

Answe is option 4)

c)
Variance = s^2 = average

Here, average = 4
So, variance = 4

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