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 ) =   = =

option 2 is correct.

step-by-step explanation:

we are given two inequality equation

x+y> 5 and -3x+2y< -2

first we draw the graph of both function using t-table method

equation: x+y> 5

for x=0, y=5

for x=-5, y=0

table:

x   :   0     5

y   :   5     0

test point (0,0) , 0> 5

false

equation: -3x+2y< -2

for x=0, y=-1

for x=2, y=4

table:

x   :   0     2

y   : -1       4

test point (0,0) , 0< -2

true

now we draw the graph. see the attachment for graph.

common region would be solution set.

option 2 is correct.

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