1. The U.S. Air Force requires that pilots have heights between 6064in. and 7577in. Heights of women are normally distributed with a mean of 6563.7in. and a standard deviation of 5 2.9in. What percentage of women meet that height requirement? (Round your answer to the nearest whole number and enter your answer in XX format)

2. To recruit more women pilots in the Air Force, if the height requirements are relaxed to allow the middle 90% 95%of women based on the height distribution ((=65,=5))(N(63.7,2.9)), what will be the heights of the shortest women meeting the requirements? (Round your answer to the nearest whole number and enter your answer in XX format)

3. What is the probability that when a value is randomly selected from a normal distribution, it is an outlier? Note: outliers are defined as data values that are above 3 Q3by an amount greater than 1.5 or below Q1 by an amount greater than 1.5, where IQRis the interquartile range. (Round your answer to three digits after decimal and write your answer in 0.XXX format.)

4. Prof. Banerjee gives a test, and the scores are normally distributed with a mean of 606070%and a standard deviation of 121210%. He plans to curve the scores.

If the grades are curved so that the grades ofBare given to scores above the bottom 70%70%and below the top 10%10%, find the new numerical limits for a grade ofB.