Question

Only c and e

(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 8.3 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) Compute the probability that mall security apprehended 9 shoplifters (use four decimals in your answer) 0.12802 Part (b) Compute the probability that mall security will apprehend at least 7 shoplifters. Enter your answer to four decimals. 0.72187 Part (c) Compute the probability that between 7 and 13 (inclusive) shoplifters will be apprehended. Enter your answer to four decimals. 0.50874 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 8.3 shoplifters and a variance of 2.88097205817759 shoplifters. B. The distribution of values is skewed to the right, with a mean of 8.3 shoplifters and a standard deviation of 2.88097205817759 shoplifters. C. The number of shoplifters apprehended each day is 8.3. D. The distribution of values is roughly symmetrical, with a mean of 8.3 shoplifters and a standard deviation of 2.88097205817759 shoplifters E. The distribution of values is roughly symmetrical, with a mean of 8.3 shoplifters and a variance of 2.88097205817759 shoplifters2. 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 (use three decimals in your answer) 3.804166 (use three decimals in your answer) 3.804166

Answer 1

c) Mean is 8.3 per day

We need to find x from 7 to 13 inclusive

P(7<I<13) = P(7) + P(8) + P(9) + P(10) + P(11) + P(12) + P(13)

P(7<< < 13) = e-8.3 8.39 7! T8! T9! 8.38 SA + + 8.310 8.311 8.312 8.313 10! 11 + 101+79) 0.677956

So, 0.678 (rounded to the 4 decimal places) is the answer.

e) mean = 8.3 per day

total opening time = 11 hours

So, mean per hour = 8.3/11 = 0.755 (rounded to 3 decimal places)

var = 0.755 (as in Poisson mean = var)

Please comment if any doubt. Thank you.