Question

In a survey with a sample of 200 private clinics, the daily number of patients treated follows a normal distribution with its mean and standard deviation as 75 and 15, respectively. What is the probability that a randomly selected clinic treats more than 80 patients in a day?

1) 0.3085
2) 0.6915
3) 0.1915
4) 0.8085

Answer 1

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.