Question

suppose you have an experiment where you flip a coin three times. you then count the number of heads.
a) state the random variable.
select an answer
rv x = the probability that you flip heads
rv x = the number of heads flipped when you flip a coin three times
rv x = flipping a coin
rv x = number of coins flipped
rv x = the number of heads flipped

c) if you were to draw a histogram for the number of heads, what shape would it be?
select an answer
d) find the mean 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 mean of a probability distribution?
which of the following is the correct interpretation of the mean?

Explanation:

Step1: Define random variable

The experiment is flipping a coin three - times and counting heads. So, the random variable $X$ is the number of heads flipped when you flip a coin three times.

Step2: Analyze histogram shape

The binomial distribution $B(n = 3,p=0.5)$ (coin - flip is a binomial experiment with $n$ trials and $p$ probability of success). For $n = 3$ and $p = 0.5$, the histogram is symmetric.

Step3: Calculate mean of binomial distribution

The formula for the mean of a binomial distribution is $\mu=np$. Here, $n = 3$ and $p=0.5$. So, $\mu=3\times0.5 = 1.5$.

Answer:

a) rv $X$ = the number of heads flipped when you flip a coin three times
c) Symmetric
d) 1.5