Samantha is a baseball player, she has a batting average of 0.280.

Question

a) find the probability that at least 3 hits in her next 5 times at bat (12 marks)
b)what is Samantha's expected number of hits in her next 10 times at bat? (3 marks)

Answer 1

Use binomial distribution, p=0.28, q=(1-0.28)=0.72
A) n=5
P(3/5)+P(4/5)+P(5/5)
=3C5*p^3*q^2 + 4C5*p^4*q^1 + 5C5*p^5*q^0
=10(0.28^3)(0.72^2) + 5(0.28^4)(0.72) + 1(0.28^5)(0.72^0)

Use your calculator to find the answer for (A)

B)
Expected value for binomial distribution with n=10, p=0.28, q=0.72 is npq
=10*0.28*0.72