Birth weight of male and female babies are normally distributed. The mean birth

Question

Birth weight of male and female babies are normally distributed. The mean birth weight of female babies is 3.2 kg with a standard deviation of 0.3 kg. The mean birth weight of male babies is 7.3 lbs with a standard deviation of 0.8 lbs. For each of the following, find the necessary z-scores, and round your answers to the nearest tenth.

a. What percent of female babies weigh more than 3.6kg?

b. What percent of male babies weigh between 6 and 8lbs?

c. What male baby weight would represent the 40th Percentile?

d. Which baby weighs more relative to their gender, a male baby that weighs 8.9 lbs or a female baby that weighs 3.7 kg?

Explanation / Answer

a)percent of female babies weigh more than 3.6kg=P(X>3.6)=P(Z>(3.6-3.2)/0.3)=P(Z>1.33)=0.0918~ 9.2%

b)percent of male babies weigh between 6 and 8lbs=P(6<X<8)=P((6-7.3/0.8<Z<(8-7.3).8)=P(-1.63<Z<0.88)

=0.8106-0.0516=0.7590 ( please try 0.7571 if tis comes wrong)

c)

for 40th percentile ; z=-0.25

hence corresponding value =mean+z*std deviation=7.3-0.25*0.8=7.1

d)

here z score for male baby=(8.9-7.3)/0.8=2

z score for female baby=(3.7-3.2)/0.3=1.67

as z score for male baby is higher ; male baby weighs more relative to their gender

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