1. 5-3 Quiz Review
1) Find the z-score that has 86.4% of the distribution area to its left.
2) Find the z-score that has 94% of the distribution area to its right.
3) Find the z-score for which 84% of the distribution’s area lies between –z and z.
4) The weights of bags of apples at Walmart are normally distributed with a mean of 5 pounds and a standard deviation of .25 pounds (4 ounces). Bags of apples are checked at the packing plant and all bags in the lowest 6% and upper 6% of weight must be rebagged. Between what two weights are the bags considered to be acceptable?
(BTW – these numbers are all made up)
5) A certain celebrity returns to their high school alma mater and promises that year’s freshman class that they will send the top 7% of that graduating class to college, all expenses paid.
a) If the mean GPA for that class is 2.56, with a standard deviation of , what is the lowest GPA that a student can have and still get college paid for?
b) If there are 256 students in the class, how many scholarships will be given?

2. 5-3 Quiz Review
1) Find the z-score that has 86.4% of the distribution area to its left.
Remember, when going to the left, or below, use the area given.
2nd VARS 3 (.864, 0, 1) = 1.098
2) Find the z-score that has 94% of the distribution area to its right.
To find the z-score or x-value to the right of or above an area, subtract that area from 1 first.
2nd VARS 3 (.06, 0, 1) =

3. 5-3 Quiz Review
3) Find the z-score for which 84% of the distribution’s area lies between –z and z.
84% of the area is between the two z-scores.
This means that 16% of the area is NOT between the two z-scores.
Since the curve is symmetrical, 8% of this area will be on each side.
.84
.08

4. 5-3 Quiz Review
3) Find the z-score for which 84% of the distribution’s area lies between –z and z.
2nd VARS 3 (.08, 0, 1) = ; (to find the lower z-score, use the area given (.08))
2nd VARS 3 (.92, 0, 1) = 1.405; (to find the upper z-score, subtract from 1)
the z-scores are and 1.405
CHECK!!
2nd VARS 2 (-1.405, 1.405, 0, 1) = , which is good enough.

5. 5-3 Quiz Review
4) The weights of bags of apples at Walmart are normally distributed with a mean of 5 pounds and standard deviation of .25 pounds (4 ounces). Bags of apples are checked at the packing plant and all bags in the lowest 6% and upper 6% of weight must be rebagged. Between what two weights are the bags considered to be acceptable?
2nd VARS 3 (.06, 5, .25) = 4.611
Again, to find the lower number, use the given percentage.
2nd VARS 3 (.94, 5, .25) = 5.389
To find the upper number, subtract the given percentage from 1.
Bags weighing between pounds and pounds are considered to be acceptable.

6. 5-3 Quiz Review
5) A certain celebrity returns to their high school alma mater and promises that year’s freshman class that they will send the top 7% of that graduating class to college, all expenses paid.
a) If the mean GPA for that class is 2.56, with a standard deviation of 1.07, what is the lowest GPA that a student can have and still get college paid for?
b) If there are 256 students in the class, how many scholarships will be given?
a) 2nd VARS 3 (.93, 2.56, 1.07) = 4.139
Since we want to be in the top 7%, we have to beat 93% of the class. Subtract given percentage from 1.
b) 256 * .07 = 17.92, or around 17.
The 18th student is not in the top 7%, and is ineligible, but if the celebrity is in a good mood might get picked anyway.