You are interested in finding out the mean number of customers entering a 24-hour convenience store every 10-minutes. You suspect this can be modeled by the Poisson distribution with a a mean of A = 3.85 customers. You are to randomly pick n = 56 10-minute time frames, and observe the number of customers who enter the convenience store in each. After which, you are to average the 56 counts you have. That is, compute the value of X. (a) What can you expect the value of f to be? 5 Enter your answer using all the decimals you can. (b) Find the value of the standard deviation of X. Enter your answer using all the decimals you can. (TX I lit (c) Find the probability that mean of the sample of 56 is between 1.4 and 4.6. If rounding only round once, at the end do not round before that. Ensure you use at least four decimals in your z-values. P(1.4 g f g 4.6) = E Use at least four decimals in your answer. (d) 92% of the time, the observed value of X will exceed what value? E- (use at least four decimals in your answer) '--ttl A-i- nu A