Question

A basket ball payer makes 90.4% of his free throws. In a game where he has 15 free throws, find the following.

a) Find the probability that he makes at least eleven free throws in that game. Write the statistical expression to represent this problem.

b) Find the mean number of free throws that he makes in that game.

c) Find the standard deviation of the number of free throws that he makes in that game.

Answer 1

Here, n = 15, p = 0.904, (1 - p) = 0.096 and x = 11
As per binomial distribution formula P(X = x) = nCx * p^x * (1 - p)^(n - x)

We need to calculate P(X > =11).
P(X <= 10) = (15C0 * 0.904^0 * 0.096^15) + (15C1 * 0.904^1 * 0.096^14) + (15C2 * 0.904^2 * 0.096^13) + (15C3 * 0.904^3 * 0.096^12) + (15C4 * 0.904^4 * 0.096^11) + (15C5 * 0.904^5 * 0.096^10) + (15C6 * 0.904^6 * 0.096^9) + (15C7 * 0.904^7 * 0.096^8) + (15C8 * 0.904^8 * 0.096^7) + (15C9 * 0.904^9 * 0.096^6) + (15C10 * 0.904^10 * 0.096^5)
P(X <= 10) = 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0.0002 + 0.0016 + 0.0089
P(X <= 10) = 0.0107

P(X >=11) = 1- P(x < =10)
= 1- 0.0107
= 0.9893

b)

mean = np
= 15 * 0.904
= 13.56

c)

std.dev =sqrt(npq)
= sqrt( 15 * 0.904 *(1-0.904))
= 1.1409