A normal human gestation period is 3743 weeks The birth weig

A normal human gestation period is 37-43 weeks. The birth weights of babies born in this range are normally distributed with a mean of 3432 grams and a standard deviation of 482 grams.

1. Find the probability that the birth weight of a randomly selected baby is

a. Less than 3000 grams

b. Greater than 4000 grams

2. What are the birth weights that define the interquartile range (IQR) of birth weights?

3. Eighty-five babies are randomly selected, and the mean weight is calculated.

a. What is the expected mean of the sample means?

b. What is the expected standard deviation of the sample means?

c. What is the shape of the distribution of the sample means?

d. What is the probability that the mean is less than 3300?

Solution

A normal human gestation period is 37-43 weeks. The birth weights of babies born in this range are normally distributed with a mean of 3432 grams and a standard deviation of 482 grams.

1. Find the probability that the birth weight of a randomly selected baby is

a. Less than 3000 grams

z value for 3000, z=(3000-3432)/482 =-0.90

P( x <3000) = P( z < -0.90)

= 0.1841

b. Greater than 4000 grams

z value for 4000, z=(4000-3432)/482 = 1.18

P( x >4000) = P( z > 1.18)

= 0.1190

2. What are the birth weights that define the interquartile range (IQR) of birth weights?

Z value for 25^th percentile = -0.674

Z value for 75^th percentile = 0.674

Q3 = 3432+0.674*482 = 3756.87

Q1= 3432-0.674*482 = 3107.13

IQR = Q3-Q1 = 3756.87-3107.13 = 649.74

3. Eighty-five babies are randomly selected, and the mean weight is calculated.

a. What is the expected mean of the sample means?

Mean = 3432

b. What is the expected standard deviation of the sample means?

Sd= sd/sqrt(n) = 482/sqrt(85) =52.2802

c. What is the shape of the distribution of the sample means?

Sample size is large( >30), the shape is approximately normal.

d. What is the probability that the mean is less than 3300?

z value for 3300, z=(3300-3432)/482 = -2.52

P( mean x <3300) = P( z < -2.52)

= 0.0059