Question

The daily number of patients in the Emergency room is assumed to be normally distributed (bell shaped curve) with a mean of 200 and a standard deviation of 30.  Answers not showing work will receive no credit.  

7. What is the probability there will be more than 250 patients? Draw a sketch along with your answer.

8. 80% of the time the daily amount of patients will be between what 2 numbers? Draw a sketch along with your answer.

    9     Would 180 patients be an outlier?

Answer 1

Solution:
Given in the question
The daily number of patients in the emergency room is assumed to be normally distributed with
Mean () = 200
Standard deviation() = 30
Solution(a)
We need to calculate probability there will be more than 250 patients i.e. P(X>250) = 1 - P(X<=250)
Here we will use the standard normal distribution, first, we will calculate Z-score as follows
Z-score = (X-)/ = (250-200)/30 = 1.67
From Z table we found a p-value
P(X>250) = 1 - 0.9525 = 0.0475
So there is a 4.75% probability that there will be more than 250 patients.
Solution(b)
We need to calculate 2 numbers for which 80% of the time the daily amount of patients will be between which can be calculated as
alpha = 0.8, alpha/2 = 0.2
For lower bound = 0.1 and upper bound = 0.9
From the Z table, we found Z-score from lower bound = -1.28155 and Upper bound Z-score = 1.28155
Lower bound X = + ZScore * = 200 - 1.28155*20 = 174.4
Upper bound X = + ZScore * = 200 + 1.28155*20 = 225.6
So 80% of the time the daily amount of patients will be between 174.4 and 225.6 patients
Solution(c)
Would 180 patients be an outliers
Z-score = (180-200)/20 = -1
as we can see the Z-score is between -2 and +2 so we can say that 180 patients are not an outlier.