Question

A certain tennis player makes a successful first serve 76​% of the time. Suppose the tennis player serves 50 times in a match.​ What's the probability that she makes at least 42 first​ serves?

Answer 1

Solution:

Given that,

P = 76% = 0.76

1 - P = 1 - 0.76 = 0.24

n = 50

Here, BIN ( n , P ) that is , BIN (50 , 0.76)

then,

n*p = 50*0.76 = 38 > 5

n(1- P) = 50*0.24 = 12 > 5

According to normal approximation binomial,

X Normal

Mean = = n*P = 50 * 0.76 = 38

Standard deviation = =n*p*(1-p) = 50*0.76*0.24 = 9.12

We using countinuity correction factor

P(X a ) = P(X > a - 0.5)

P(x > 41.5) = 1 - P(x < 41.5)

= 1 - P((x - ) / < (41.5 - 38) / 9.12)

= 1 - P(z < 1.159)

= 1 - 0.8768   

= 0.1232

Probability = 0.1232

The probability that she makes at least 42 first​ serves is 0.1232