# statistics probability

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 55 but less than 95 will wait more than 30 minutes?

the answers are:

a. 0.468

b. 0.185

c. 0.999

I think I have to somehow find the mean and standard deviation, and then find the z-score, and look up from the normal distribution table to find the probability. however, I don't know how to find the mean and standard deviation just by having the median.

### 1 Answer

- 知足常樂Lv 76 years agoFavorite Answer
Ho Yin, this is actually a nice question.

It makes use of normal approximation to binomial probabilities.

For B(n, p), when n is large and when p is close to 0.5, the normal approximation N(np, np(1-p)) works wells.

圖片參考：http://imgcld.yimg.com/8/n/HA00430218/o/2014020513...