The Normal Distribution

Question

The weights for newborn babies is approximately normally distributed with a mean of 6.1 pounds and a standard deviation of 1.9 pounds.

Consider a group of 800 newborn babies:

1. How many would you expect to weigh between 4 and 8 pounds? 

2. How many would you expect to weigh less than 7 pounds? 

3. How many would you expect to weigh more than 5 pounds? 

4. How many would you expect to weigh between 6.1 and 10 pounds? 

HINT: Do not round until you get your final answer.

Answer 1

If you look at the normal distribution curve.

-1σ =34.13% --> 4.2 - 6.1 lbs

+1σ=34.13% --> 6.1 - 8 lbs

+1σ-+2σ = 13.59% --> 8 - 10 lbs

+2σ-+3σ = 2.14% --> 10-11.7 lbs

1) 4 thru 8 lbs

(34.13%+34.13%)×800 ≈ 514 babies

2) Less than 7 lbs

(50%+34.13%)×800 ≈ 673 babies

3) More than 5 lbs

(50%+34.13%)×800 ≈ 673 babies

4) Between 6.1 and 10 lbs

(34.13% + 13.9%)×800 ≈ 384 babies