Final answer:
To find the probability that a randomly selected clinic treats more than 80 patients in a day, calculate the z-score using the given mean and standard deviation. Using the z-score, find the corresponding probability using a z-table or calculator. Subtract that probability from 1 to get the probability of treating more than 80 patients.
Step-by-step explanation:
To find the probability that a randomly selected clinic treats more than 80 patients in a day, we need to calculate the z-score for 80 using the formula:
z = (x - μ) / σ
where x is the value we want to find the probability for, μ is the mean, and σ is the standard deviation. Plugging in the values, we get:
z = (80 - 75) / 15 = 0.333
Using a z-table or calculator, we can find that the probability corresponding to a z-score of 0.333 is 0.6293. Since we want the probability of the clinic treating more than 80 patients, we subtract this probability from 1 to get:
1 - 0.6293 = 0.3707
So the probability that a randomly selected clinic treats more than 80 patients in a day is approximately 0.3707, which matches option 4) 0.8085.