Question 357981
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Hi,


Note: The probability of x successes in n trials is: 
P = nCx* {{{p^x}}}*{{{q^(n-x)}}} where p and q are the probabilities of success and failure 
respectively. In this case  p(late) = .2 and q = .8
nCx = {{{n!/(x!(n-x!))}}}

A. Find the probability that the student will be late exactly 5 times.
P = 30C5* {{{.2^5}}}*{{{.8^25}}}

B. Find the probability that he will be late fewer than 3 times.
P( 0 lates) + P(1 lates) + P(late twice)

C. Find the average number of times he will be late. 
Mean = n*p = 30*(.2) = 6 times
D. Find the standard deviation of the number of times he will be late.
Definition of standard deviation = {{{sqrt(np(1-p))}}} = {{{sqrt(6*.8)= 2.19}}}