Assuming a normal distribution, 75% of patients will wait at least this much time?

Question

Your primary care doctor's office staff has determined the average wait time to see the doctor is 18 minutes, with a standard deviation of 7 minutes.

 

Assuming a normal distribution, 75% of patients will wait at least this much time?

 

Need how you used the excel formula and how you got the answer. Thanks

Answer 1

Prob ( X> k) = 0.75

 

1 - Prob(X < k) = 0.75 <---- property of normal probability

 

1 - Prob( Z < (k-18)/7 ) = 0.75 <--- changes to z score

 

1 - 0.75 = Prob( Z < (k-18)/7 )  <--- solves for the unknown probability

 

0.25 = Prob(Z < (k-18)/7)

 

Reading the normal distribution table in reverse,

the value with this probability is -0.665

 

-0.665 = (k-18)/7

 

k = 7 * -0.665 + 18 = 13.345

 

75% of the patients will wait at least 13 minutes and 21 seconds or longer