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Sati [7]
3 years ago
8

A researcher wishes to conduct a study of the color preferences of new car buyers. Suppose that 50% of this population prefers t

he 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.
Mathematics
1 answer:
Artyom0805 [142]3 years ago
7 0

Answer:

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 ) = n_C_r \times p^{r}\times q^{n-r}

So, P ( X = 15 ) =  {20}_C_{15} \times 0.5^{15}\times 0.5^{20-15} = {20}_C_{15} \times 0.5^{15}\times 0.5^{5} = 0.0148

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