Question

Jill’s bowling scores are approximately normally distributed with mean 170 and standard deviation 20, while Jack’s scores are approximately normally distributed with mean 160 and standard deviation 15. If Jack and Jill each bowl one game, then assuming that their scores are independent random variables, approximate the probability that
(a) Jack’s score is higher;
(b) the total of their scores is above 350.

Answer 1

Answer:

0.3446,0.2119

Step-by-step explanation:

Given that Jill’s bowling scores are approximately normally distributed with mean 170 and standard deviation 20, while Jack’s scores are approximately normally distributed with mean 160 and standard deviation 15.

If X represents Jill scores and Y Jack scores we have

X is N(170,20) and Y is N(160,15)

since x and y are independent we have the difference

X-Y is $N(170-16,\sqrt{20^2+15^2} )\\=N(10, 25)$

a) Prob that Jack’s score is higher

= P(-x+y>0)

=$P(Z<\frac{10}{25} )\\= P(Z<0.4)\\\\= =0.3446$

b) X+Y is Normal with (330, 25)

$P(X+Y>350) = P(Z>\frac{350-330}{25} )\\=P(Z>0.8)\\\\= =0.2119$