Statistics

Given a normal distribution of the lengths of wing-spans of a certain butterfly has a mean of 20 mm and standard deviation 3.5 mm.  Find, ROUNDING YOUR ANSWERS TO 4 DECIMAL PLACES.

1. The area under the standard normal curve to the left of 26.5 

2. The area under the standard normal curve to the right of 9 

3. The area under the standard normal curve between 10 and 30 

4. The area under the standard normal curve either to the left of 9.5 or to the right of 30.5 

5. The area under the standard normal curve at 20 

6. What wing-span has an area of 0.0401 on it left side under the standard normal curve? 

7.  What wing-span has an area of 0.1005 on it left side under the standard normal curve? 

8. What wing-span has an area of 0.0480 on it right side under the standard normal curve? 

The average credit card debt for college seniors is $3262. If the debt is normally distributed with a standard deviation of $1100, find these probabilities.

1. The senior owes less than $1000. 

2. The senior owes more than $4000. 

3. The senior owes between $3000 and $4000 

4. The senior owes less than $1000 or more than $4000 

5.  The senior owes exactly $2500 

6. What is the minimum amount a senior needs to owe to be considered a senior with debt in the top 10%? 

7. What is the maximum a senior needs to owe to be considered a senior with debt in the bottom 1%? 

(ROUND ALL ANSWERS TO 4 DECIMAL PLACES. NO EXCEPTIONS!!)