Carlton and Leon are expert bowlers. Seventy percent of Carlton's rolls are strikes, while 67% of Leon's rolls are strikes. Suppose that Carlton and Leon each bowl 25 games. What is the probability that Leon's proportion of strikes is greater than Carlton's for these games?

The probability that Leon strikes is greater than Carlton strike is 0.40905

Step-by-step explanation:

From the question, we have;

The percentage of Carlton's rolls are strikes, = 70%

The number of games Carlton played, n₁ = 25

The percentage of Leon's rolls that are strikes, = 67%

The number of games Leon played, n₂ = 25

Therefore, we have;

Where;

k₁ = 0.7 × 25 = 17.5

k₂ = 0.67 × 25 = 16.75

The test statistic is given as follows;

From the z-table, we have;

The p-value for Carlton strikes is greater than Leon's strike = 0.59095

∴ The p-value for Leon strikes is greater than Carlton strike = 1 - 0.59095 = 0.40905

The probability that Leon strikes is greater than Carlton strike = 0.40905