Final answer:
The student's question involves calculating the probability that exactly 5 out of 14 people own an HDTV using the binomial probability formula. We use the given success rate of 37% and the formula to compute the desired probability.
Step-by-step explanation:
The student is asking a probability question related to binomial distribution. In this scenario, we are given that 37% of people own an HDTV and are asked to find the probability that exactly 5 out of 14 randomly selected people own an HDTV. To solve this, we use the binomial probability formula:
P(X=k) = (n choose k) * p^k * (1-p)^(n-k)
Where:
- n is the number of trials (14 people surveyed)
- k is the number of successes we want to find the probability for (5 people owning an HDTV)
- p is the probability of a single success (37% or 0.37)
- 1-p is the probability of a single failure
Plugging in the values, we get:
P(X=5) = (14 choose 5) * 0.37^5 * (1-0.37)^(14-5)
After calculating this, we would have the probability that exactly 5 out of 14 people own an HDTV.