Consider a basketball game where a player throws from the free throw line. Her success rate is 65%. If she throws 10 times in a game determine the following:The mean and standard deviation of this binomial distribution.
You know that p=.65 and q =.35 and n=10
Mean is np
SD = the square root of (npq)
1.508
To determine the mean and standard deviation of a binomial distribution, you need to know the probability of success (p) and the number of trials (n). In this case, the probability of success is 65% or 0.65, and the number of trials is 10.
1. Mean (μ):
The mean of a binomial distribution is calculated by multiplying the probability of success (p) by the number of trials (n). So in this case, the mean (μ) is:
μ = p * n = 0.65 * 10 = 6.5
Therefore, the mean is 6.5.
2. Standard Deviation (σ):
The standard deviation of a binomial distribution is calculated using the formula:
σ = sqrt(n * p * (1 - p))
where sqrt denotes the square root, n is the number of trials, and p is the probability of success.
σ = sqrt(10 * 0.65 * (1 - 0.65))
= sqrt(10 * 0.65 * 0.35)
= sqrt(2.275)
Using a calculator or software, we can find:
σ ≈ 1.51
Therefore, the standard deviation is approximately 1.51.
So, the mean of this binomial distribution is 6.5, and the standard deviation is approximately 1.51.