Question

Sam 'Vandelay' Johnson plays basketball for his college team. You've observed that the probability of Sam making a given shot is 0.6 and that the success of a given shot is independent of other shots. Over the course of many games, Sam takes 80 attempted shots at the basket. Let W be the random variable that is the number of successful shots.

You should use the normal approximation to the binomial to calculate the probabilities in parts b) and c). Give your answers as decimals to 4 decimal places.

a)Find the probability that Sam makes exactly 44 successful shots from the 80 attempts.

P(W = 44) =

b)Find the probability that Sam makes at most 44 successful shots from the 80 attempts.

P(W ≤ 44) =

c)Find the probability that Sam makes between 40 and 50 successful shots from the 80 attempts.

P(40 ≤ W ≤ 50) =

Answer 1

Given that n = 80 and p = 0.6

Using normal approximation to binomial

mean = n*p

= 80*0.6 = 48

standard deviation = sqrt{n*p*(1-p)}

= sqrt{80*0.6*0.4} = 4.382

(A) P(X=44) = P(43.5<X<44.5)

using normalcdf

setting lower = 43.5, upper = 44.5, mean = 48 and sd = 4.382

P(X=44) = normalcdf(43.5,44.5,48,4.382)

= 0.0600

(B) P(X less than equal to 44) = P(X< 44.5)

using normalcdf

setting lower = -99, upper = 44.5, mean = 48 and sd = 4.382

P(X less equal to 44) = normalcdf(-99,44.5,48,4.382)

= 0.2122

(C)

using normalcdf

setting lower = 39.5, upper = 50.5, mean = 48 and sd = 4.382

P(X=44) = normalcdf(39.5,50.5,48,4.382)

= 0.6896