An internal study by the technology services department at lahey electronics revealed company employees receive an average of 4.3 non-work-related e-mails per hour. assume the arrival of these e-mails is approximated by the poisson distribution. what is the probability linda lahey, company president, received exactly 4 non-work-related e-mails between 4 p. m. and 5 p. m. yesterday? (round your probability to 4 decimal places.) what is the probability she received 7 or more non-work-related e-mails during the same period? (round your probability to 4 decimal places.) what is the probability she received three or less non-work-related e-mails during the period? (round your probability to 4 decimal places.)

P(4 non-work-related e-mails)=0.1933

P(7 or more non-work-related e-mails)=0.1442

P(3 or less non-work-related e-mails)=0.3771

Step-by-step explanation:

A Poisson distribution is useful to measure the probability of a number of events in a given period, in this problem, receiving a non-work-related e-mail would be the event and an hour would be the period of time.

Its probability mass function is , being k the number of events and  λ how many sucesses (events) are per period of time (4.3 in this case)

First, we calculate what is the probability of receiving exactly 4 e-mails:

As k is a discrete variable, to know the joint probability of different number of events we add the probability of each value.

The probability of receiving 7 or more is the sum of P(7), P(8), ..., P(∞):

Last, the probability of receiving 3 or less is the sum of P(0), P(1), P(2) and P(3):