3. There are 156 Radio City Music Hall Rockettes in all of the traveling companies + the performers in New York. Assume the heights of the dancers are normally distributed with an average of 5.7 feet and a standard deviation of 0.07 feet (a) What is the range of heights (minimum and maximum ) for the center 95% of Rockettes?

(b) What is the range of heights (minimum and maximum) for the center 99.7% of Rockettes?

(c) If a Rockette is 5.75 feet tall, what is her z score?

(d) If a Rockette is 5.7 feet tall, what is her z score?

(e) What percent of Rockettes are taller than 5.7 feet?

(f)What percent of Rockettes are between 5.6 and 5.8 feet tall?

(g ) How many Rockettes are shorter than 5.8 feet (round your answer to the nearest whole Rockette)?

(h) A Rockette at the 25th percentile is how tall?

(i) A Rockette at the 75th percentile is how tall?

(j) A Rockette at the 50th percentile is how tall?