Question

Based on data from a large study of healthy infants in six countries, the World Health Organization produced growth charts that are part of every pediatrician’s toolkit for monitoring a child’s overall health. According to the WHO report, girls who are one month old have a mean head circumference of 36.6 centimeters with a standard deviation of 1.2 centimeters. As with most body measurements, head circumference has a normal probability distribution. Medscape defines microcephaly (small head syndrome) as a head circumference that is more than two standard deviations below the mean. What is the probability that a one-month old girl will be categorized as having microcephaly?

Answer 1

Answer:

1.1375%

Step-by-step explanation:

If the measurements follow a normal distribution, then

100%-95.45% = 4.55%

must be outside the interval  

[mean-2 times standard deviation, mean+2 times standard deviation]

= [36.6-2(1.4), 36.6+2(1.4)]

(see picture attached)

Of this 4.55%, 2.275% is less than 36.6-2(1.4) (microcephaly) and 2.275% is greater than  36.6+2(1.4) (macrocephaly)

Supposing half of these children are girls, we have a probability of 1.1375%

So, the probability that a one-month old girl will be categorized as having microcephaly is 1.1375%, that is to say 11,375 one-month-old girls out of 1,000,000 will probably be categorized as  having microcephaly.