Question

bell - shaped

d) find the mean number of heads.

round final answer to 3 decimal places. write your units in the second box.

1.500 heads

which of the following is the correct symbol for the mean of a probability distribution?

which of the following is the correct interpretation of the mean?

if you flip a coin 3 times over and over, you can expect to get an average of 1.5 heads for every 3 flips

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:

Step1: Identify the distribution

This is a binomial distribution problem. For a binomial distribution \(X\sim B(n,p)\), the formula for the standard deviation is \(\sigma=\sqrt{np(1 - p)}\). Here, \(n = 3\) (number of coin - flips) and \(p=\frac{1}{2}\) (probability of getting a head in a single coin - flip).

Step2: Substitute values into the formula

Substitute \(n = 3\) and \(p=\frac{1}{2}\) into the formula \(\sigma=\sqrt{np(1 - p)}\). First, calculate \(np(1 - p)\):

$$
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Then, find the square root: \(\sigma=\sqrt{\frac{3}{4}}=\frac{\sqrt{3}}{2}\approx0.866\)

Answer:

0.866, heads