Question

I have a statistics math problem. if someone could answer. "A basketball player makes 70% of free throws. he throws 15 free shots. what is the probability that the basketball player makes 7 or more free shots inside basket."

Answer 1

The requirements for an experiment's to be considered binomial are:
1. probability of success remains constant throughout the experiment
2. all trials are independent and random
3. the number of trial is constant and known.

This problem satisfies the requirements for the binomial distribution, which gives the probability of r successes out of n trials each with a probability of p as:
P(r)=C(n,r)p^r(1-p)^(n-r).
where for the present case,
C(n,r)=combination of r object out of n
=n!(r!(n-r)!)
p=0.7
n=15
r=7,8,9,...15
so
P(X>=7)=ΣP(r), r=7 to 15
=P(X=7)+P(X=8)+...P(X=15)
=0.03477+0.08113+0.14724+0.20613+0.21862+0.17004+...+0.00475
=0.98476