The number of emails that I get in a weekday (Monday through Friday) is denoted

Question

The number of emails that I get in a weekday (Monday through Friday) is denoted by X with an average of 10 emails per hour. The number of emails that I receive on weekends (Saturday and Sunday) is denoted by Y with an average of 6 emails per hour. Considering there are 52 weeks in year, 30 days a month and considering 5 working days each week, a. What is the probability that the average number of emails I get over weekday is no more than average emails over weekends in a month? b. What is the probability that the average number of emails I get over weekday is no more than average emails over weekends in a year?

Explanation / Answer

a. if a month has 30 days, and an average of 4 weeks a month, then the no of weekdays in a month will be given as: 5*4 =20. then the no of weekends in the month will be 10 days.

then X= 20*10 = 200 hours and Y= 10*6 =60 hours

the total number of emails expected to be recieved in the month = 200 + 60 =260 emails

the probability that the number of emails I get over weekday is no more than the average emails over the weekend in a month = 200/260 = 10/13

b. if a year has 52 weeks, and each week has 5 days and 2 weekends, then:

the number of weekdays in the whole year = 52*5 =260

and the number of hours, during the weekdays, in the whole month = 260*24 =6240 hours

the number of weekends in the whole year = 52*2 = 104

and the number of hours, during the weekdays, in the whole month = 104*24 =2496 hours

no of emails expected during the weekdays for the whole year = 6240*10=62400 emails

no of emails expected during the weekends for the whole year = 2496*6= 14976

total no of emails expected during the year = 62400 + 14976 = 77376 emails

so, the probability that the average number of emails i get over the weekday is no more than the weekends = 62400/77376 =25/31

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