Question

e) find the standard deviation for the number of heads. round final answer to 3 decimal places. write your units in the second box.

Explanation:

1. Assume a binomial - distribution scenario:

• If we are flipping a fair coin \(n\) times, the number of heads \(X\) follows a binomial distribution \(X\sim B(n,p)\), where \(p = 0.5\) (probability of getting a head in a single fair - coin flip). The formula for the standard deviation of a binomial random variable is \(\sigma=\sqrt{np(1 - p)}\).
• However, since the number of coin - flips \(n\) is not given in the problem, let's assume a general case for now.
• Let's say we flip a coin \(n\) times.
• The probability of getting a head \(p = 0.5\) and the probability of getting a tail \(1 - p=0.5\).

1. Calculate the standard deviation:

• Substitute \(p = 0.5\) and \(1 - p = 0.5\) into the standard - deviation formula \(\sigma=\sqrt{np(1 - p)}\). We get \(\sigma=\sqrt{n\times0.5\times0.5}=\sqrt{0.25n}=0.5\sqrt{n}\).
• Without knowing the value of \(n\), we can't give a numerical answer. But if we assume \(n = 10\) (for example, if the context was 10 coin - flips):
• \(\sigma=\sqrt{10\times0.5\times0.5}=\sqrt{2.5}\approx1.581\).

Since the number of coin - flips \(n\) is not given in the problem, we can't provide a definite numerical answer. If we assume \(n = 10\) (just for illustration purposes), the standard deviation is approximately \(1.581\) (units: number of heads).

Step1: Identify the distribution

Assume coin - flips follow a binomial distribution \(X\sim B(n,p)\) with \(p = 0.5\).

Step2: Apply the standard - deviation formula

Use \(\sigma=\sqrt{np(1 - p)}\), substituting \(p = 0.5\) gives \(\sigma = 0.5\sqrt{n}\).

Step3: Provide an example

If \(n = 10\), then \(\sigma=\sqrt{10\times0.5\times0.5}=\sqrt{2.5}\approx1.581\).

Answer:

If \(n = 10\), the standard deviation is approximately \(1.581\), units: number of heads.