Final answer:
To find the probability that exactly 5 out of 10 students call home every weekend when the chance is 45%, we use the binomial probability formula. The calculated probability is approximately 0.1865, which is option b.
Step-by-step explanation:
The question asks for the probability that exactly 5 out of 10 randomly selected students will say they call home every weekend, given that 45% of students do so. We can solve this using the binomial probability formula, which is:
P(X = k) = (n choose k) * p^k * (1-p)^(n-k)
Where:
- n = total number of trials (in this case, n = 10)
- k = number of successes (in this case, k = 5)
- p = probability of success on a single trial (in this case, p = 0.45)
- (1-p) = probability of failure on a single trial
Plugging the values into the formula, we calculate:
P(X = 5) = (10 choose 5) * (0.45)^5 * (0.55)^5
After calculation, the closest answer to the provided choices would be option b. 0.1865.