Question

I Need help with e), can someone show me how to do it by hand?

(1 point) On a typical day at a local popular mall, the number of shoplifters caught by mall security fluctuates from day to day, with an average of 8.2 caught per day. Suppose you are to count the number of shoplifters apprehended at this mall today. (Assume today is a typical day at the mall.) Part (a) What is the probability that mall security apprehended 8 shoplifters? 0.1392 (use four decimals in your answer) Part (b) What is the probability that mall security will apprehend at least 7 shoplifters. Enter your answer to four decimals 0.7104 Part (c) Find the probability that between 5 and 13 shoplifters will be apprehended. Enter your answer to four decimals. 0.8708 Part (d) Think about the distribution of the number of shoplifters mall security apprehends on a typical day. What can you say about this distribution? Select the most appropriate reason below A. The distribution of values is skewed to the right, with a mean of 8.2 shoplifters and a standard deviation of 2.86356421265527 shoplifters. O B. The distribution of values is skewed to the right, with a mean of 8.2 shoplifters and a variance of 2.86356421265527 shoplifters C. The number of shoplifters apprehended each day is 8.2. D. The distribution of values is roughly symmetrical, with a mean of 8.2 shoplifters and a variance of 2.86356421265527 shoplifters. O E. The distribution of values is roughly symmetrical, with a mean of 8.2 shoplifters and a standard deviation of 2.86356421265527 shoplifters. Part (e) On a typical day, the mall is open from 10:00am to 9:00pm, a total of 11 hours.You are interested in the number of shoplifters apprehended in any given hour How many shoplifters would you expect mall security to catch in any given hour? Provide the variance of this count as well. μ = 3.758 (use three decimals in your answer) 3.758 ii: (use three decimals in your answer)

Answer 1

The Mean and Variance of a Poisson Distribution are equal to λ, where λ is the average number of successes within a given region

We have the average per day is 8.2

i.e, 24 hours - λ=8.2

For 11 hours, λ=?

On solving we have, λ=11*8.2/24 = 3.758

As explained above, both mean and variance are the same

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