Question

According to a study, the median time a patient waits to see a doctor in an emergency room is 30 minutes. Consider an emergency room on a day when 150 patients visit. a. What is the probability that more than half will wait more than 30 minutes? b. What is the probability that more than 80 will wait more than 30 minutes? c. What is the probability that more than 60 but less than 90 will wait more than 30 minutes? III. a. The probability is (Round to three decimal places as needed.)

Answer 1

The probability that more than half of the patients will wait more than 30 minutes is approximately 0.0169

To solve this problem, we need to use the normal distribution.

Given that the median time a patient waits to see a doctor in an emergency room is 30 minutes, we can assume that the waiting time follows a normal distribution with a mean of 30 minutes.

a. To find the probability that more than half will wait more than 30 minutes, we need to find the probability that a random variable, representing the number of patients waiting more than 30 minutes, is greater than 75.

Using the normal distribution, we can calculate this probability as:

P(x > 75) = P(Z > (75 - 150*0.5) / sqrt(150*0.5*0.5)) = P(Z > 2.12) = 1 - P(Z < 2.12) = 1 - 0.9831 = 0.0169

Therefore, the probability that more than half of the patients will wait more than 30 minutes is approximately 0.0169