1. Probability Question About an “individual” About a “statistic”
Use population distribution
Use s
Must be told if the distribution is normal
About a “statistic”
Use sampling distribution
Use SE
CLT tells if normal
If the relevant distribution is NOT normal then the probability can NOT be computed.
Sampling Distributions

2. A company is investigating the number of sick days used by each of its employees. Assume that the population is right-skewed with a mean of 7 and a standard deviation of 2 days.
What symbol would you put on the 7?
What symbol would you put on the 2? m s
Sampling Distributions
Sampling Distributions
Slide #2

3. A company … population is right-skewed … m=7, s=2 days.
For each question determine …
Which distribution would be used to answer the question
The specifics of that distribution
If the question can be answered
What is the probability of observing a mean of 6.4 days or less in a random sample of 25 workers?
Sampling distribution (about a mean)
CLT says … may not be normal, mean=7, SE=2/sqrt(25)
Should not (sampling distribution not known to be normal)
Sampling Distributions
Sampling Distributions
Slide #3

4. A company … population is right-skewed … m=7, s=2 days.
For each question determine …
Which distribution would be used to answer the question
The specifics of that distribution
If the question can be answered
What is the probability of observing a mean of 6.4 days or less in a random sample of 36 workers?
Sampling distribution (about a mean)
CLT says …`x~N(7,2/sqrt(36))
Can ... distrib(6.4,mean=7,sd=2/sqrt(36))
Sampling Distributions
Sampling Distributions
Slide #4

5. A company … population is right-skewed … m=7, s=2 days.
For each question determine …
Which distribution would be used to answer the question
The specifics of that distribution
If the question can be answered
What is the probability of observing a worker using fewer than 5 sick days?
Population distribution (about an individual)
Background says … right-skewed, mean=7, SD=2
NO (population distribution not normal)
Sampling Distributions
Sampling Distributions
Slide #5