In general, if X has the binomial distribution with n trials and a success probability of p then

P[X = x] = n!/(x!(n-x)!) * p^x * (1-p)^(n-x)

for values of x = 0, 1, 2, …, n

P[X = x] = 0 for any other value of x.

this is found by looking at the number of combination of x objects chosen from n objects and then a total of x success and n – x failures.

the mean of the binomial distribution is n * p

the variance of the binomial distribution is n * p * (1 – p)

Find P(X ≤ 6)

= P(X = 0) + P(X =1) + P(X = 2) +P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6)

= 0.01801440 + 0.08106479 + 0.17226269 + 0.22968358 + 0.21532836 + 0.15072985 + 0.08164534

= 0.948729