one of de moivre other finding isthat for events that are approximated by a bell curve roughly 95 percents of the data falls within two standard deviation of the mean. the range of values within two standard deviations of the mean is the95 percents confidence interval .find the mean and standard dviation for the number of the heads when flippnig 3200 coins?
To find the mean and standard deviation for the number of heads when flipping 3200 coins, we can use the Bernoulli distribution.
The Bernoulli distribution describes the probability of obtaining a "success" (in this case, a head) in a single trial with a binary outcome (head or tail), assuming the probability of success is constant.
The mean, denoted by μ (mu), of a Bernoulli distribution is equal to the probability of success. In this case, the probability of getting a head in a single coin flip is 1/2. Therefore, the mean μ = 1/2.
The standard deviation, denoted by σ (sigma), of a Bernoulli distribution can be calculated using the formula:
σ = √(p * (1 - p))
Where p is the probability of success. In this case, p = 1/2.
σ = √(1/2 * (1 - 1/2))
= √(1/2 * 1/2)
= √(1/4)
= 1/2
So the mean μ = 1/2 and the standard deviation σ = 1/2 for the number of heads when flipping 3200 coins.