Question 820390
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Hi,
Re Reply, must refer You further to stattrek.com for their excellent tutorials
Formulas given below for Poisson and Binomial Distributions give a <u>singular probability</u>.
As  all but one of the problems involved cumulative probabilities: Recommend using Ti Calculator to retrieve answers:
If You do not have access to a Ti Calculator, recommend stattrek.com (choosing Stat Tables will give you access to calculators
(also a good reference to check your Ti Calculations while You learn how to use it)
According to a survey, college students make an average of 11 calls per day on their mobile
 phone. Moreover, 80% of the students surveyed indicated that their parents pay for their
 mobile phone expenses.
 (a) If a student is selected at random, what is the probability that he or she makes:
<u>POISSON Distribution</u> P(x; &#956;) = (e^(-&#956;) (&#956;^x) / x! where  &#956;  is the average number of successes  
x is the actual number of successes that result from the experiment, e  approximately equal to 2.71828. 
for ex: &#956;  = 11   P(x = 6) = {{{e^(-11)(11^6)/6!}}} 
 (i) More than 12 calls in a day? 0.31130334853593   Ti: 1- poissioncdf(11, 12)
 P(x>12) = 1 - [P(1)+P(2)+P(3)+P(4)+P(5)+P(6)+P(7)+P(8)+P(9)+P(10)+P(11)+P(12)]
 (ii) Less than the average number of calls in a day? 0.459888702693687 poissioncdf(11, 10)
P(x<11) = [P(1)+P(2)+P(1)+P(3)+P(4)+P(5)+P(6)+P(7)+P(8)+P(9)+P(10)]
 (iii) More than 15 calls in a day? 0.092603908284245  Ti: 1- poissioncdf(11, 15)
<u>BINOMIAL Distribution</u> P(x) = nCx* {{{p^x*q^(n-x)}}} 
where p and q are the probabilities of success and failure respectively. 
In this case p = .80 & q = .20 & n = 20   nCx = {{{n!/(x!(n-x)!)}}}
For ex:  b (i),    P(20) ={{{ (.80)^20}}}
 (b) If 20 students are selected at random, what is the probability that:
 (i) All 20 have their parents pay for their mobile phone expenses? 0.0115292150460685 Ti binomcdf(20, .80, 20).
 (ii) At least 8 have their parents pay for their mobile phone expenses?0.999984837159687  Ti 1 - binomcdf(20, .80, 7).
  1 - [P(1)+P(2)+P(3)+P(4)+P(5)+P(6)+P(7)]
 (iii) No more than 5 students pay for their own mobile phone expenses?0.804207785459551  Ti binomcdf(20, .20, 5).
[P(1)+P(2)+P(3)+P(4)+P(5)]