


Sherril M. Stone, Ph.D. 

Department of Family Medicine 

OSUCollege of Osteopathic Medicine 






Probability  fraction or proportion of an
outcome in a population 



Example 1  A, B, C, or D = 6 A's, 3 B's, 10 C's
and 9 D's 



Probability of A = #
of AÕs
= p(A) = 6 

# of possible
outcomes
28 



Example 2  probability of tossing coin and
getting heads = 1 = .50 

2 





Random Sampling Ð equal chance of being selected 

Constant probability Ðsampling with replacement 



Example 1 Ð draw a jack of clubs = 1 

52 



Example 2 Ð draw a jack of hearts = 1
51 

(if jack of clubs not returned to deck) 






Symmetrical distribution Ð aka Bellshaped curve 

Largest frequency of data occurring at the
middle 

Mean = Median = Mode 

Area under the curve = 1.00 





1.00 







μ 



The area between the mean and one SD above the
mean = .3413 

Unit Normal Distribution  normal distribution
based on zscores 





Standardizes your data distribution 

Convert raw scores into zscores 

If X = 10, SD = 2, X = 11.7 



z = 11.7  10 = 1.7
= .85 

2
2 

Use z Table to find area under bell curve 

1st column is zscore 

2nd column is proportion between mean and z 

3rd column is proportion in the tail beyond z 




SD
= 1 



.5000
.3023 .1977 



___________________________________________ 

3
2
1
0
1 2
3
zscores 





.85 

X = 11.7 

z = .85 

p(X > 11.7) = .1977 









Sample Means (X) 

should pile around population mean (m) 

should produce a normal distribution curve 

larger the sample n, the closer to m 

lower sample n, more widely scattered
scores 









1 2 3 4 5 

Sample Xs 






CLT 

for any m and s, distribution of X and SD approaches normal distribution
as n approaches infinity 

N > 30 Ð distribution is almost normal 

Standard error Ð measures difference between X
and m 

Rule of large numbers 

as samples sizes increase, the error decreases 

n = 1, large error (n = 1, error = SD) 

SE
= s 

…n 





Standard Deviation 

measures standard distance between X and m (X  m) 

measure of variability of population scores 

Standard Error 

measures standard distance between X and m 

measure of variability of sample
scores 

measures reliability (similar scores each time) 

Sampling error Ð discrepancy between the X and m 


