For tasks 7-12, assume that the time interval between customers entering your store can be modeled using an exponential distribution. you know that you have an average of 4 customers per minute, so the rate is 4, or you can say that lambda = 4 according to yakir (2011, p. 79-80).

it is easiest to keep everything in the original units of measurement (minutes), but you can also translate that to seconds because a rate of "4 customers per minute" is the same as "4 customer per 60 seconds," and you can divide each number by 4 to get a rate of "1 customer per 15 seconds" or a rate of "1/15 customers per second."

7) what is the expectation for the time interval between customers entering the store? be sure to specify the units of measurement in your answer (see yakir, 2011, pp. 79-80). round to 3 decimal places:

8) what is the variance of the the time interval? be sure to specify the units of measurement in your answer. round to 3 decimal places:

9) the pexp() function is introduced at the bottom of yakir, 2011, p. 79, and there are some tips above. what is the probability that the time interval between customers entering the store will be less than 15.5 seconds. be sure to enter values so that everything is in the same unit of measurement. be sure to specify the units of measurement in your answer. round your answer to 3 decimal places:

10) what is the probability that the time interval between customers entering the store will be between 10.7 seconds and 40.2 seconds (see yakir (2011, p. 79-

11) the qexp() function in r allows you to enter a probability, and it will tell you the criterion value ("cutoff point") that corresponds to that probability value (e. g., if you enter .05 it tells you the cutoff point below which 5% of the values in the distribution fall).

what value of x would be the criterion value (cut-off point) for the top 5% of time intervals (round to 3 decimal places, and include the units of measurement)?



12) describe in your own words the meaning of the number that the following r command produces (you are asked to interpret the resulting number so that we understand what that number means).