Z-Scores
A distribution of scores has a mean of 32 and a standard deviation of 12. What z-score corresponds to a score of 54.
Z=+1.5
What is the main reason normal distributions are importnat in the field of statitistics?
What happens to the shape of a binomial distribution as the sample size (n) gets larger?
becomes more normally distributed
A population or sample distribution is a distribution of people or things. What is the binomial distribution a distribution of?
A distribution of probabilities
Mean of a political science test is 85 with a standard deviation of 5. What proportion of people scored between 75 and 98?
75-85/5 = -2 = 0.0228
98-85/5 = +2.6 = 0.9953
0.9953-0.0228 = 0.9725
In a perfectly symmetrical normal distribution curve, Matt is exactly at the mean. What is the percentile rank?
50th percentile. This means 50% of the data is below the mean and 50% is above the mean.
If the probability of getting 10 heads is so small, what do we mean when we say "we expect to get 10 heads"?
It means that the mean of the distribution is 10 heads
You take a die and paint four of its sides red. You then roll it 72 times. What is the probability that you will get 50 or more reds?
EV = N*P = 72*2/3 =48
SE = sqrt (72*2/3*1/3) = sqrt(16) = 4
Z=x-mean/SE = 50-48/4 = 1/2 OR 0.50 --> 0.3085
The mean of political science test is 85 and the standard deviation is 5. It is normally distributed. Tabitha got a z-score of +0.54. What is her test score?
87.7
Assuming the test score distribution is normal, what is the IQR of the scores given that the mean is 840 and the standard deviation is 60?
Z= +0.67 or -0.68 (acceptable)
Z = -0.67 or +0.68 (acceptable)
-0.68*60+840 = 799.2
+0.68*60+840 = 880.8
880.8-799.2= 81.6 OR 80.4 (if used 0.67)
Yes or No. Would rolling a die and counting the number of dots give us a binomial distribution?
No. There are more than 2 categories!
You take a die and paint four of its sides red. How many rolls are necessary in order for us to appropriately use the normal distribution? (Hint 72 was enough!)
(hint: use the liberal or conservative rule!)
1/3*N > 5 (liberal) = 15
1/3*N > 10 (conservative) = 30
The mean of a political science test is 85 with a standard deviation of 5. Camry ranks in the 62nd percentile. What is a possible score for them?
62nd percentile has a z-score of 0.31, 0.32, or 0.33 (all acceptable)
0.32*5+85 = 86.6
In a perfectly symmetrical normal distribution curve, Sandy scores exactly one standard deviation above the mean. What is her percentile?
84th percentile! WHY?
The empirical rule states that approximately 68% of the data falls within one standard deviation of the mean.
This means that 34% of the data is between the mean and one standard deviation above the mean. Since 50% of the data is below the mean you add that to the 34% above the mean (50%+34%=84%).
Therefore, the percentile Sandy scores in is approximately the 84th percentile.
If you roll a die five times, what is the probability of getting a "one" exactly twice?
P= 1/6 | X=2 | n=5
5!/2!3! * 1/6^2 * 5/6^3 --> 10*(1/36)*(125/216) = 1250/7776 OR 0.16075
What is the probability of rolling a die 180 times and getting more than 38 "ones"?
EV =180*1/6 = 36
SE = sqrt(180*1/6*5/6) = 5
38-36/5 = 1.6 = 0.0548