The Normal Distribution

Question

The weights for newborn babies is approximately normally distributed with a mean of 5.4 pounds and a standard deviation of 1.4 pounds.

Consider a group of 1200 newborn babies:

1. How many would you expect to weigh between 6 and 9 pounds? 

2. How many would you expect to weigh less than 8 pounds? 

3. How many would you expect to weigh more than 7 pounds? 

4. How many would you expect to weigh between 5.4 and 10 pounds?

Answer 1

1. P(6<x<9) = P((9-5.4)/1.4) - P((6-5.4)/1.4) = 0.3291

0.3291*1200 = 394.92, or 395 rounded to one whole baby.

2. P(x<8) = P((8-5.4)/1.4) = 0.9684

0.9684*1200 = 1162.08, or 1162 rounded to the nearest baby.

3. P(x>7) = P((7-5.4)/1.4) = 0.1265

0.1265*1200 = 151.8, or 152 rounded to the nearest baby.

4. P(5.4<x<10) = P((10-5.4)/1.4) - P((5.4-5.4)/1.5)

= 0.4995

0.4995*1200 = 599.4, or 599 rounded to the nearest baby.