## Question 379:

1

1. First, lookup the z-score corresponding to the top 30% of area under the normal curve, which is the same as 70% of the total area. Use the percentile to z-score calculator and enter .70 for 1-sided area. You should get a z-score of .524
2. Now setup an equation and solve for this z-score of .524, using the formula of a z-score= (datapoint-mean)/standard deviation = z-score
3. ( x - 300 )/80 = .524
1. 80*.524 = x -300
2. 41.92 = x-300
3. 341.92 =x
4. So a score of around 342 will get you in the top 30%

The interquartile range is the 75th percentile minus the 25th percentile. You can visualize this range by using the interactive graph of the standard normal curve. Enter the mean of 300 and SD of 80 in the 2-sided area graph.

To find the value follow the same procedures as above by finding the z-scores for the 75th and 25th percenile using the percentile to z-score calculator . The 75th percentile has a z-score of of .675.

1. ( x - 300 )/80 = .675
2. 80*.675 = x -300
3. 54 = x-300
4. 354 =x

The 25th percentile has a z-score of -0.675

1. ( x - 300 )/80 = -.675
2. 80*-.675 = x -300
3. -54 = x-300
4. 246 =x

So the interquartile range is between 246 and 354, which contains 50% of the values.