If boys and girls are equally likely and groups 400 births are randomly selected find the standard deviation
Standard deviation = √npq = √[(400)(.5)(.5)] = √(100) = 10
Note: n = sample size, p = .5, q = .5
could you please break this answer down, I'm not sure how you got .5. please
To find the standard deviation, we need more information about the probability of boys and girls being born. Without this information, it is not possible to calculate the standard deviation. Please provide the probability of a boy or girl being born.
To find the standard deviation, we need to know the probability of an event occurring. In this case, let's assume that the probability of a child being born as a boy or a girl is 50% each, meaning both outcomes are equally likely.
Now, if we randomly select 400 births, we can use the binomial distribution formula to calculate the standard deviation.
The formula for the standard deviation of a binomial distribution is given as:
σ = √(n * p * q)
Where:
σ is the standard deviation
n is the number of trials
p is the probability of success
q is the probability of failure (1 - p)
In this case,
n = 400 (as we are selecting 400 births)
p = 0.5 (probability of a child being born as a boy or girl)
q = 1 - p = 1 - 0.5 = 0.5 (probability of a child not being born as a boy or girl)
Now, we can plug in the values into the formula:
σ = √(400 * 0.5 * 0.5) = √(100) = 10
Therefore, the standard deviation for randomly selecting 400 births where boys and girls are equally likely is 10.