## Answers

it is a binomial probability distribution, because there is fixed number of trials,

only two outcomes are there, success and failure

trails are independent of each other

and probability is given by

P(X=x) = C(n,x)*p^{x}*(1-p)^{(n-x)} |

where

Sample size , n = 153

Probability of an event of interest, p = 0.63

a)

P(no less than 87) = P(X≥87) = ΣC(n,x)*p^{x}*(1-p)^{(n-x)} where x goes from 87 to 153

P(x≤87) = ΣC(153 ,x)*0.63^{x}*(1-0.63)^{(153-x)} where x goes from 87 to 153

b)

expected users = np =153 * 0.63 = 96.39

c)

Binomial to normal approximations using continuity

Sample size , n = 153

Probability of an event of interest, p = 0.63

right tailed

X ≥ 87

Mean = np = 96.39

std dev ,σ=√np(1-p)= 5.9720

P(X ≥ 87 ) = P(Xnormal ≥ 86.5 )

Z=(Xnormal - µ ) / σ = -1.656

=P(Z ≥ -1.656 ) = **0.9511 (answer)**