Calculate The Z-Score For an Outcome X
Determine the Z-Score of X = 20
What (whole number) Z-score is greater than approximately 16% of all outcomes?
Z = -1
What two outcomes hold 68% of the data between them?
X = 17 and X = 27
Z = 0
The number standard deviations above or below the mean for a specific outcome X
Determine the Z-score of 22.5
Z=.1
Name two z-scores that have 34% of all outcomes between them.
Z = 0 and Z = 1
or
Z = 0 and Z=-1
What two outcomes hold 95% of the data between them?
X = 12 and X = 32
What Z-score did we establish as having 2.5% of the data below it, before we introduced the Z-table?
Z = -2
What does the standard deviation measure about a data set?
The average distance from the mean for data points, or how "spread out" the data is.
Determine the Z-score of 16.26
-.748
Which Z-score is greater than 31.92% of all outcomes?
Z=-.48
Outcome X = A is greater than 80% of the data, while Outcome X = B is greater than 50% of the data. What is the percent chance of an outcome occurring between the two?
30%
Determine the percentage of data below an outcome with Z = 1.55
93.94%
When we plug a Z-score into the Z-Table, what does the number provided to us actually represent?
The proportion/percentage of data below that position on the normal curve.
Given a new average of 148 with a standard deviation of 28.5, determine the Z-score for X = 100
Z=-1.68
Which outcome X is greater than 12.1% of all other outcomes?
X = 14.15
Given that outcome C has a z-score of 1.4 and outcome D has a z-score of -.8, what is the percent chance of an outcome occurring between them?
70.73%
Determine the percentage of data ABOVE the outcome X = 24
42.07%
Why does the average go in the middle of the normal curve?
Because the average has the statistically highest chance of occurring, so it must line up with the highest probability on the normal curve.
A professional golfer has an average score of 70.25 across all games played, with a standard deviation of 4.5. What would the Z-score be for his result of 72?
Z=.39
Josiah finds himself in a bidding war for a vehicle on the market. After doing some research, he determines that the car has an average sale price of $42,000 with a standard deviation of $1600.
The opposition proposes a price that is larger than 88.1% of all expected prices. What was their proposed price?
$43,888
38.48%
Landon collects a variety of Marvel action figures in their free time, the value of which is quite high. The average item in his collection has a price of $680, and standard deviation of $120.
What is the percent chance of an item in his collection costing MORE than $560?
Approximately 84%
Determine the Z-score for each of them, then determine the percentage associated with both Z-scores using the Z-table, then subtract one percentage from the other