# Chapter 1. Finding a value given a proportion

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Stat Tutor
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1:03

### Question 1.1

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Incorrect. Cumulative proportions are found in the center of the Standard Normal table. So to find a cumulative proportion, we look in the center and read the z-score in the margins.
Correct. Cumulative proportions are found in the center of the Standard Normal table. So to find a cumulative proportion, we look in the center and read the z-score in the margins.
Incorrect. Try again.
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2:12

### Question 1.2

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Incorrect. Before looking up the given proportion inside the table, you must first convert it to a cumulative proportion.
Correct. Before looking up the given proportion inside the table, you must first convert it to a cumulative proportion.
Incorrect. Try again.
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5:04

### Question 1.3

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Incorrect. The first quartile, Q1, has area of 25% less than it and 75% of the area greater than it.
Correct. The first quartile, Q1, has area of 25% less than it and 75% of the area greater than it.
Incorrect. Try again.
2

### Question 1.4

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Incorrect. 90% is area on the right. To get cumulative area, we subtract 90% from 100% to get 10% or 0.1000
Correct. 90% is area on the right. To get cumulative area, we subtract 90% from 100% to get 10% or 0.1000
Incorrect. Try again.
2

### Question 1.5

Incorrect. 40% is area on the left, so the cumulative area is 40% or 0.4000.
Correct. 40% is area on the left, so the cumulative area is 40% or 0.4000.
Incorrect. Try again.
2

### Question 1.6

Incorrect. 100% – 60% = 40%; dividing 40% by 2 to get the area in the lower tail, we get 20% or 0.2000.
Correct. 100% – 60% = 40%; dividing 40% by 2 to get the area in the lower tail, we get 20% or 0.2000.
Incorrect. Try again.
2

### Question 1.7

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Incorrect. Since cumulative areas are given inside the table, we locate the cumulative area and read the corresponding z-score in the left and top margins.
Correct. Since cumulative areas are given inside the table, we locate the cumulative area and read the corresponding z-score in the left and top margins.
Incorrect. Try again.
2

### Question 1.8

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Incorrect. z-scores are given in the left and top margins of the table.
Correct. z-scores are given in the left and top margins of the table.
Incorrect. Try again.
2

6:19

### Question 1.9

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Incorrect. This is a correct statement.
Correct. This is a correct statement.
Incorrect. Try again.
2

### Question 1.10

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Incorrect. This is a correct statement.
Correct. This is a correct statement.
Incorrect. Try again.
2

### Question 1.11

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Incorrect. First of all 0.73 is a cumulative area. The closest area to 0.7300 in the table is 0.7291. This corresponds to z = 0.61.
Correct. First of all 0.73 is a cumulative area. The closest area to 0.7300 in the table is 0.7291. This corresponds to z = 0.61.
Incorrect. Try again.
2

### Question 1.12

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First of all 28% is area on the right. To find the cumulative area, subtract 28% from 100% to get 72%. Looking up 0.7200, we find .7257 as the closest. This corresponds to z = 0.60.
Correct. First of all 28% is area on the right. To find the cumulative area, subtract 28% from 100% to get 72%. Looking up 0.7200, we find .7257 as the closest. This corresponds to z = 0.60.
Incorrect. Try again.
2

12:10

### Question 1.13

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Incorrect. 68% of the Math SAT scores are between 400 and 600. 100% minus 68% equals 32%. So the area below 400 plus the area above 600 equals 32%. Half of that is the area above 600. So, 16% of the scores are above 600.
Correct. 68% of the Math SAT scores are between 400 and 600. 100% minus 68% equals 32%. So the area below 400 plus the area above 600 equals 32%. Half of that is the area above 600. So, 16% of the scores are above 600.
Incorrect. Try again.
2

### Question 1.14

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Incorrect. 50% of the area is less than 500. Between 500 and 600 is half of 68% or 34% of the area. 50% plus 34% = 84%. So, 84% of the scores are less than 600.
Correct. 50% of the area is less than 500. Between 500 and 600 is half of 68% or 34% of the area. 50% plus 34% = 84%. So, 84% of the scores are less than 600.
Incorrect. Try again.
2

### Question 1.15

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Incorrect. Since 79.1% of the scores are below the score of interest, we know that .7910 is a cumulative area. Looking up .7910 inside the table gives us a z-score of 0.81. We find x = µ + zσ = 500 +.81(100) = 581.
Correct. Since 79.1% of the scores are below the score of interest, we know that .7910 is a cumulative area. Looking up .7910 inside the table gives us a z-score of 0.81. We find x = µ + zσ = 500 +.81(100) = 581.
Incorrect. Try again.
2

### Question 1.16

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Incorrect. Since 24.2% of the scores are above the score of interest, we know that .2420 the area on the right and is not a cumulative area. To get the cumulative area, we subtract .2420 from 1 to get 0.7580. Looking up .7580 inside the table gives us a z-score of 0.70. We find x = µ + zσ = 500 +.70(100) = 570.
Correct. Since 24.2% of the scores are above the score of interest, we know that .2420 the area on the right and is not a cumulative area. To get the cumulative area, we subtract .2420 from 1 to get 0.7580. Looking up .7580 inside the table gives us a z-score of 0.70. We find x = µ + zσ = 500 +.70(100) = 570.
Incorrect. Try again.
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