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=4.21

=4.21customers. You are to randomly pick=50

n=5010-minute time frames, and observe the number of customers who enter the convenience store in each. After which, you are to average the 50 counts you have. That is, compute the value ofX.

(a)What can you expect the value ofXto be?

(b)Find the value of the standard deviation of

X=

(c)Find the probability that mean of the sample of 50 is between 2.9 and 4.7. If rounding only round once, at the end do not round before that. Ensure you use at least four decimals in your

z-values.

(2.94.7)=

(d)92% of the time, the observed value of

Xwill exceed what value?