Question

If a baseball player's batting average is 0.340 ( i.e., the probability of getting a hit each time at bat is 0.340), find the probability that the player will have a bad season and get at most 60 hits in 200 times at bat?

Answer 1

We have given that,

$n = 200$

$p = 0.34$

$x=$ number of hits

$n=$ total times at bat

We know,

$\mu = np = 200 \times 0.34 = 68$

$\sigma = \sqrt{npq} = \sqrt{200 \times 0.34 \times 0.66} = 6.6993$

Applying continuity correction,

$z = \dfrac{x-\mu}{\sigma}$

$z = \dfrac{60-68}{6.6993} = -1.12$

For the normal standard distribution,

$P(z < - 1.12) = 13.14$ %