Question

Jeff's bowling scores are approximately normally distributed with mean 130 and standard deviation 15, while Jill's scores are normally distributed with mean 125 and standard deviation 24. If Jeff and Jill each bowl one game, then assuming that their scores are independent random variables, approximate the probability that the total of their scores is above 260.

Answer 1

Here, μ = 130 + 125 = 255,
σ = sqrt(14^2 + 25^2) = 28.3019 and x = 260. We need to compute P(X >= 260). The corresponding z-value is calculated using Central Limit Theorem

z = (x - μ)/σ
z = (260 - 255)/28.3019 = 0.18

Therefore,
P(X >= 260) = P(z <= (260 - 255)/28.3019)
= P(z >= 0.18)
= 1 - 0.5714
= 0.4286