Question

Waiting times are normally distributed in a hospital emergency room, with a mean of 120 minutes and a standard deviation of 30 minutes.

1. If you select 100 patients at random, what is the probability that the mean of their waiting times will be less than 115?
   
   
   
   
   
   
   
   
   
   
   
   
2. If you select 900 patients at random, what is the probability that the mean of their waiting times will be less than 115?
   
   
   
   
   
   
   
   
   
   
   
   
3. Based upon (a) and (b), what do you conclude about the relationship between sample size and the likelihood of drawing a sample whose mean is far from the population mean?
   
   
   
   
4. Again with respect to waiting times, with a random sample of 100, what is the probability of drawing a sample with a mean that is between 115 and 117?
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
5. And again with a sample of 100, what is the probability of drawing a sample with a mean that is between 117 and 121?
   
   
   
   
   
   
   

6. In the field of public health, a needs assessment is a process that is designed to “identify problems and assess a community’s capacity to address health and social service needs.” (publichealthdatastandards.info).

You are responsible for a needs assessment of individuals living with HIV in NYC. To gather data, you survey a random sample of individuals who visit a hospital on the Upper East Side for a check-up last week. How might your sampling strategy influence your findings?

Answer 1

Answer)

As the data is normally distributed we can use standard normal z table to estimate the answers

Z = (x-mean)/(s.d/√n)

Given mean = 120

S.d = 30

A)

P(x<115)

Z = (115 - 120)/(30/√100) = -1.67

From z table, P(z<-1.67) = 0.0475

B)

Z = (115-120)/(30/√900) = -5

From. z table, P(z<-5) = 0

C)

As the sample size increases, probability decreases

D)

P(115<x<117) = P(x<117) - P(x<115)

P(x<117)

Z = (117 - 120)/(30/√100) = -1

From z table, P(z<-1) = 0.1587

P(x<115) = 0.0475

Required probability is 0.1587 - 0.0475 = 0.1112