Question

Computer help hot line reccives, on average, 6 calls per hour asking for assistance. the distribution is poisson. for any randomly selected hour, find the probability that the company will receive a. at least 6 calls b. 4 or more calls c. at most 5 calls

Answer 1

To find the probability of receiving a certain number of calls per hour using the Poisson distribution, calculate the cumulative distribution function for specific ranges.

Step-by-step explanation:

To find the probability that the company will receive at least 6 calls in a randomly selected hour, use the Poisson distribution with an average rate of 6 calls per hour. The formula to calculate this probability is P(X >= k) = 1 - P(X < k), where X is the random variable and k is the number of calls. In this case, k is 6. Using the Poisson cumulative distribution function on a graphing calculator, P(X >= 6) is approximately 0.1606.

To find the probability that the company will receive 4 or more calls, use the Poisson cumulative distribution function with a range of 4 to infinity. For this calculation, P(X >= 4) is approximately 0.7119.

To find the probability that the company will receive at most 5 calls, use the Poisson cumulative distribution function with a range of 0 to 5. For this calculation, P(X <= 5) is approximately 0.5598.