230k views
1 vote
The weights for newborn babies is approximately normally distributed with a mean of 5.8 pounds and a standard deviation of 2.1 pounds.

Consider a group of 1100 newborn babies:

1. How many would you expect to weigh between 4 and 7 pounds?

2. How many would you expect to weigh less than 6 pounds?

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

4. How many would you expect to weigh between 5.8 and 10 pounds

User Divina
by
7.5k points

1 Answer

2 votes

Answer:

Explanation:

To find the number of newborn babies weighing between 4 and 7 pounds, we need to calculate the z-scores for these two weights and use the normal distribution table.

For 4 pounds: z = (4 - 5.8) / 2.1 = -0.857

For 7 pounds: z = (7 - 5.8) / 2.1 = 0.571

Using the normal distribution table, the area between z = -0.857 and z = 0.571 is 0.5418.

So, the expected number of newborn babies weighing between 4 and 7 pounds is:

0.5418 x 1100 = 596 (rounded to the nearest whole number)

To find the number of newborn babies weighing less than 6 pounds, we need to calculate the z-score for 6 pounds and use the normal distribution table.

z = (6 - 5.8) / 2.1 = 0.095

Using the normal distribution table, the area to the left of z = 0.095 is 0.5375.

So, the expected number of newborn babies weighing less than 6 pounds is:

0.5375 x 1100 = 591 (rounded to the nearest whole number)

To find the number of newborn babies weighing more than 5 pounds, we need to calculate the z-score for 5 pounds and use the normal distribution table.

z = (5 - 5.8) / 2.1 = -0.381

Using the normal distribution table, the area to the right of z = -0.381 is 0.6499.

So, the expected number of newborn babies weighing more than 5 pounds is:

0.6499 x 1100 = 715 (rounded to the nearest whole number)

To find the number of newborn babies weighing between 5.8 and 10 pounds, we need to calculate the z-scores for these two weights and use the normal distribution table.

For 5.8 pounds: z = (5.8 - 5.8) / 2.1 = 0

For 10 pounds: z = (10 - 5.8) / 2.1 = 1.905

Using the normal distribution table, the area between z = 0 and z = 1.905 is 0.4713.

So, the expected number of newborn babies weighing between 5.8 and 10 pounds is:

0.4713 x 1100 = 518 (rounded to the nearest whole number)

User TManhente
by
6.7k points