Question 924880
p(pass) = .8 , n = 7
P(x = 5) = 7C5(.8)^5(.2)^2
or
Using a TI calculator 0r similarly a Casio fx-115 ES plus
P(x = 5) = binompdf(7, .8, 5) = .275

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P(fewer than half pass) = P( x ≤ 3)   3 would be fewer than half
 Using a TI calculator 0r similarly a Casio fx-115 ES plus
P( x ≤ 3) = binomcdf(7, .8,3) = .033
Highly Recommend Using a Calculator for cumulative binomial Probabilities
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0r by hand..
P( x ≤ 4) = P(0) + P(1) +P(2) +P(3)  
Using: {{{P (x)= highlight_green(nCx)(p^x)(q)^(n-x) }}}