Question 2. In a random survey of 3,015 boys age 11, the average height was 146 cm, and the standard deviation (SD) was 8 cm. A histogram suggested the heights were approximately normally distributed. Fill in the blanks-
a. The height of a boy 1 SD above average is _____________ cm.
b. Another boy was 148 cm tall. He was above average by __________ SDs.
c. A third boy was 1.5 SDs below the average height. He was __________ cm tall.
d. If a boy was within 2.25 SDs of average height, the shortest he could have been is __________ cm and the tallest is __________ cm.
e. Here are the heights of four boys: 150 cm, 130 cm, 165 cm, 140 cm. Which description from the list below best fits each of the boys (a description can be used more than once)? Justify you answer.
- Unusually short.
- About average.
- Unusually tall.