The average weight of babies born in a full term pregnancy (between 37-43 weeks)

Question

The average weight of babies born in a full term pregnancy (between 37-43 weeks) is normally distributed with a mean weight of 3500 grams and a standard deviation of 600 grams. Using this information calculate:

a. The probability that the birth weight of a randomly selected baby exceeds 4000 grams

b. The probability that the birth weight of a randomly selected baby is between 3000 and 4000 grams

c. The probability that the birthweight of a randomly selected baby is either less than 2000 grams or greater than 5000 grams

d. How would you characterize the 25th percentile of full term baby weights

Explanation / Answer

Answer:

The average weight of babies born in a full term pregnancy (between 37-43 weeks) is normally distributed with a mean weight of 3500 grams and a standard deviation of 600 grams. Using this information calculate:

a. The probability that the birth weight of a randomly selected baby exceeds 4000 grams

z value for 4000, z =(4000-3500)/600 = 0.83

P( x >4000) = P( z > 0.83) = 0.2033

b. The probability that the birth weight of a randomly selected baby is between 3000 and 4000 grams

z value for 3000, z =(3000-3500)/600 = -0.83

P( 3000<x<4000) = P( -0.83<z<0.83) = P( z <0.83) – P( z < -0.83)

=0.7967-0.2033

=0.5934

c. The probability that the birthweight of a randomly selected baby is either less than 2000 grams or greater than 5000 grams

z value for 2000, z =(2000-3500)/600 = -2.5

z value for 5000, z =(5000-3500)/600 = 2.5

P( x <2000 or x >5000) = P( z <-2.5 or z >2.5)

=P( z <-2.5)+P( z >2.5) =0.0062+0.0062

=0.0124

d. How would you characterize the 25th percentile of full term baby weights

z value for 25th percentile =-0.674

x =3500-0.674*600

=3095.6 grams

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