Question

A certain tennis player makes a successful first serve 74​% of the time. Suppose the tennis player serves 110 times in a match.​ What's the probability that she makes at least 86 first​ serves?

Answer 1

Solution :

Given that,

p = 0.74

q = 1 - p = 1 - 0.74 = 0.26

n = 110

Using binomial distribution,

Mean = = n * p = 110 * 0.74 = 81.4

Standard deviation = = n * p * q = 110 *0.74 *0.26 = 4.60

P(x 86 ) = 1 - P(x   86 )

= 1 - P[(x - ) / (86 - 81.4) / 4.60 ]

= 1 -  P(z 1.00)

= 1 - 0.8413

= 0.1587