Question

c) if you were to draw a histogram for the number of heads, what shape would it be? bell - shaped. d) find the mean number of heads. round final answer to 3 decimal places. write your units in the second box. 0.500 × 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. e) find the standard deviation for the number of heads. round final answer to 3 decimal places. write your units in the second box. which of the following is the correct symbol for the standard deviation of a probability? f) find the probability of having two or less heads. 7/8

Explanation:

Step1: Recall binomial distribution formula for mean

For a binomial distribution $X\sim B(n,p)$, the mean $\mu = np$. Here, $n = 3$ (number of coin - flips) and $p=\frac{1}{2}$ (probability of getting a head in a single fair - coin flip).
$\mu=np=3\times\frac{1}{2}=1.500$

Step2: Recall binomial distribution formula for standard deviation

The standard deviation $\sigma=\sqrt{np(1 - p)}$. Substitute $n = 3$ and $p=\frac{1}{2}$ into the formula.
$\sigma=\sqrt{3\times\frac{1}{2}\times(1 - \frac{1}{2})}=\sqrt{\frac{3}{2}\times\frac{1}{2}}=\sqrt{\frac{3}{4}}\approx0.866$

Answer:

d) Mean number of heads: 1.500, no units (it's a pure number in this context)
e) Standard deviation of number of heads: 0.866, no units (it's a pure number in this context)