To find the probability of exactly 8 buyers preferring brown out of 18 selected, we can use the binomial probability formula:
P(X = k) = (n choose k) * p^k * (1-p)^(n-k)
where:
n = total number of buyers selected = 18
k = number of buyers preferring brown = 8
p = probability of preference for brown = 0.30
(1-p) = probability of not preferring brown = 0.70
Plugging in the values:
P(X = 8) = (18 choose 8) * 0.30^8 * 0.70^(18-8)
P(X = 8) = (18! / (8!(18-8)!) * 0.30^8 * 0.70^10
P(X = 8) = (48620) * 0.30^8 * 0.70^10
P(X = 8) = (48620) * 0.006561 * 0.028248
P(X = 8) = 36.845
Therefore, the probability that exactly 8 buyers would prefer brown out of 18 selected is approximately 0.0068 rounded to four decimal places.
A researcher wishes to conduct a study of the color preferences of new car buyers. Suppose that 30%
of this population prefers the color brown. If 18
buyers are randomly selected, what is the probability that exactly 8
buyers would prefer brown? Round your answer to four decimal places.
1 answer
1 answer