Suppose you have an experiment where you toss a fair coin three times. You then count the number of heads observed over those three tosses. Use this experiment to address each of the following questions. Round solutions to three decimal places, if necessary.

a) State the random variable.

Select an answer

X = the number of heads observed

X = number of coins tossed

X = the number of heads observed when you flip a coin three times

X = the probability that you observe heads

X = tossing a coin

b) Construct a probability distribution table for the number of heads obtained over three tosses. Enter thex

x

-values from smallest to largest.

x

x

P

(

x

)

P(x)

c) Determine the shape of the probability distribution ofx

x

.

The probability distribution ofx

x

isSelect an answer

Right-skewed

Left-skewed

Uniform

Symmetric

.

d) Find the mean number of heads for this distribution.

=

=

The mean of adiscreteprobability distribution is also notated bySelect an answer

s

N

X

E(x)

n

X

.

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

Select an answer

Every time you flip a coin 3 times you will get heads most of the time

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

Every time you flip a coin 3 times you will get 1.5 heads

e) Find the standard deviation for the number of heads for this distribution.

=

=

f) Find the probability of obtaining one or less heads over three tosses of a coin.

P

(

P(

one or less heads)

=

)=