In a certain country, the mean birth weight for boys is 3.23kg, with a standard
ID: 3176945 • Letter: I
Question
In a certain country, the mean birth weight for boys is 3.23kg, with a standard deviation of 0.58kg. Assuming that the distribution of birth weight is approximately normal, complete parts a through e below.
a. A baby is considered of low birth weight if it weighs less than 2.5kg. What proportion of baby boys in this country are born with low birth weight?The proportion of baby boys that are born with a low birth weight is _____ %. (Round to one decimal place as needed.)
b. What is the z-score for a baby boy that weighs1.5kg (defined as extremely low birth weight)?The z-score is ______ (Round to two decimal places as needed.)
c. Typically, birth weight is between 2.5kg and 4.0kg. Find the probability a baby is born with typical birth weight.The probability that a baby is born with typical birth weight is_____ %. (Round to one decimal place as needed.)
d. Matteo weighs 3.5kg at birth. He falls at what percentile?The percentile that Matteo falls at is _____ (Round to one decimal place as needed.)
Explanation / Answer
Mean is 3.23 and SD is 0.58
a) P(x<2.5) =?
z value is (2.5-3.23)/0.58 =-1.26
thus P(z<-1.26)=1-P(z<1.26), from normal distribution table, we get 1-0.8962 =0.1038
b) for 1.5kg, z value is (1.5-3.23)/0.58=-2.98
c) we know the z for 2.5, for 4 it is given by (4-3.23)/0.58 =1.33
P(-1.26<z<1.33)=P(z<1.33)-(1-P(z<1.26))
from normal distribution table we get 0.6293-0.1038=0.5255
d) P(x<3.5)=P(z<(3.5-3.23)/0.58)=P(z<0.47)
from normal distribution table we get 0.6808