1.Ravi's math contest result put him in the 97th percentile. If 4000 students competed, how many had a score higher than Ravi's score?

2.Suppose X~N(50, 42 ). What value of x would have a z-score of 2.10?

3.The maximum attention spans, in seconds, of 40 two-year-olds are normally distributed with a mean of 75 and a standard deviation of 10. How many of these toddlers will have an attention span of less than 71 s?

4.The lengths of sunfish in Grenadier Pond are normally distributed with a mean of 15 cm. Find the standard deviation, to one decimal place if 91% of these fish have a length less than 17.7 cm.

5.The volumes of apple juice in cartons are normally distributed with a standard deviation of 120 mL. Find the mean, to the nearest whole number, if 34% of these cartons contain less that 961 mL of juice.

6.A manufacturer of mens' pants knows that the waist measurements of men (in inches) are normally distributed with a mean of 34 and a standard deviation of 3.2. To guarantee that the middle 95% of men can buy a pair of his pants that are not too small, what whole-number sizes must be manufactured?

7.Both Aaron and Marie, who attended different schools, finished grade 12 with final averages of 82. The mean of these averages in Aaron's school was 65 and the standard deviation was 10. In Marie's school, the mean was 68 and the standard deviation was 8. Use z-scores to determine who had the better mark.

8.For X~N(18, 5 ), find the value of x that corresponds to the 29th percentile.

9.What percent of baseball players' games last between 2.5 h and 3.5 h if the lengths of games are normally distributed with a mean of 2.7 h and a standard deviation of 0.5 h?