A tennis player makes a successful first serve 70% of the time.If she serves 80 times,is it appropriate to use a Normal model to approximate the distribution of the number of good first serves? Assume that each serve is independent of the others.
A)No; Normal model cannot be used to approximate the distribution because nq

Question

A tennis player makes a successful first serve 70% of the time.If she serves 80 times,is it appropriate to use a Normal model to approximate the distribution of the number of good first serves? Assume that each serve is independent of the others.
A)No; Normal model cannot be used to approximate the distribution because nq < 10.
B)Yes; Normal model with μ = 56 and σ = 16.80 can be used to approximate the distribution.
C)Yes; Normal model with μ = 56 and σ = 4.10 can be used to approximate the distribution.
D)Yes; Normal model with μ = 24 and σ = 16.80 can be used to approximate the distribution.
E)No; Normal model cannot be used to approximate the distribution because np < 10.

Quizplus · Accepted Answer

The conditions for using the Normal approximation to the binomial distribution are n*p >= 10 and n*(1-p) >= 10. In this case, n = 80 and p = 0.7, so both these conditions are satisfied (n*p = 56 and n*(1-p) = 24). Therefore, we can use the Normal model with mean μ = n*p = 56 and standard deviation σ = sqrt(n*p*(1-p)) = 4.10 to approximate the distribution of the number of good first serves.

A Tennis Player Makes a Successful First Serve 70% of the Time.If