Question

A researcher wishes to conduct a study of the color preferences of new car buyers. suppose that 50% of this population prefers the color green. if 16 buyers are randomly selected, what is the probability that exactly 9 buyers would prefer green? round your answer to four decimal places.

Answer 1

To solve this question, use the Binomial probability formula.

The formula is given by

$^nC_xp^x(1-p)^{n-x}$

Where:

n = the number of trials

x = the sample we aim to try

p = the probability of success

In this question:

n = 16

x = 9

p = 0.5

Substituting in the equation:

$\begin{gathered} ^nC_xp^x(1-p)^{n-x} \\ ^{16}C_9*0.5^9(1-0.5)^{16-9} \\ \end{gathered}$

And the combination formula:

$^nC_x=\frac{n!}{(n-x)!*x!}$

Then:

$\begin{gathered} \frac{16!}{(16-9)!*9!}*0.5^9(1-0.5)^{16-9} \\ \frac{16!}{7!*9!}*0.5^9*0.5^7 \\ 11440*0.00195*0.0078 \\ =0.1746 \end{gathered}$

Answer: The probability is 0.1746.