A researcher wishes to conduct a study of the color preferences of new car buyers. Suppose that 50% of this population prefers the color red. If 20 buyers are randomly selected, what is the probability that exactly 15 buyers would prefer red? Round your answer to four decimal places.

Probability that exactly 15 buyers out of 20 will prefer red is 0.0148.

Step-by-step explanation:

This problem has binomial probability distribution.

So probability of success ( population preferring Red colour) i.e.  p = 50% = 0.5

therefore probability of failure ( population preferring  other colors ) i.e. q = 1 - p = 1 - 0.5 = 0.5

20 buyers are selected at random, therefore n = 20.

We need to find the probability that exactly 15 buyers would prefer red and so r = 15 and it is given by,

P( X = r ) =

So, P ( X = 15 ) =   = =

the system of inequity is

step-by-step explanation:

from the given graph it is noticed that we have two related lines. one is solid and another is dashed.

if a line passing through two points, then the equation of line is

the solid line passing through the points (0,4) and (4,0).

the related equation of solid line is .

similarly, find the related equation of dashed line. the dashed liune passing through the points (0,0) and (3,1).

the related equation of dashed line is

from the given graph it is noticed that the point (0,1) lies on the shaded region, therefore the point (0,1) must be satisfied by the related equations.

check the related equations by the point (0,1).

this statement is true if the sign of inequality is < instead of equality. since it is an solid line therefore the sign of inequality will be . the required inequality is

similarly, check the second related equation.

it is a dashed line, so this statement is true if the sign of inequality is > . the required inequality is