Suppose the mean weight of newborns is 75 lbs and the SD is

Suppose the mean weight of newborns is 7.5 lbs. and the SD is 0.35 lbs. The medical community believes that babies with weight at the top 3% should receive a special treatment. How much should a baby weigh in order to qualify? In other words, what is the cutoff weight? (For the sake of the example, ignore variations in weight due to gender or height)

Solution

X : weight of the baby

P( X >x) = 0.97

P( Z > ( x - 7.5) / 0.35) = 0.97

(x - 7.5)/0.35 = Z0.97

(x - 7.5)/0.35 = -1.881

x = 7.5 - (1.881 × 0.35)

x = 6.84

The baby should weigh 6.84lbs