statistics questions based on babies and birth weight

Question

The weights for newborn babies is approximately normally distributed with a mean of 6.2 pounds and a standard deviation of 1.8 pounds.

Consider a group of 1100 newborn babies:

1. How many would you expect to weigh between 3 and 7 pounds? 

2. How many would you expect to weigh less than 5 pounds? 

3. How many would you expect to weigh more than 4 pounds? 

4. How many would you expect to weigh between 6.2 and 10 pounds? 

Answer 1

Hi Wendy!

1. Since the the z-scores for this question are so far apart (z = -24 and z = 16), P(-64 < x < 16) = 1, so I would expect ALL babies to weigh between 3 and 7 pounds.
2. Since the corresponding z-score is so small (z = -24), P(x < -24) = 0, so I would expect NONE of the babies to weigh less than 5 pounds.
3. Since the the z-score is so small (z = -44) and we are looking for the probability GREATER than this value, P(x > -44) = 1 - P(x < -44) = 1, so I would expect ALL babies to weigh more than 4 pounds.
4. Since the z-scores for this question are z = 0 and z = 76, P(0 < x < 76), I would expect 50% (or approximately 550 babies) to weigh between 6.2 and 10 pounds.