Question

A certain tennis player makes a successful first serve 61​% of the time. Suppose the tennis player serves 70 times in a match.​ What's the probability that she makes at least 56 first​ serves? The probability she makes at least 56 first serves is nothing.

Answer 1

Solution :

Given that,

p = 0.61

q = 1 - p =1-0.61=0.39

n = 70

Using binomial distribution,

= n * p = 70*0.61=42.7

= n * p * q = 70*0.61*0.39=4.0808

Using continuity correction

,P(x >56 ) = 1 - P(x <55.5 )

= 1 - P((x - ) / < (55.5-42.7) / 4.0808)

= 1 - P(z <3.14 )   

Using z table   

= 1-0.9992

probability= 0.0008