Question

According to the World Health Organization (WHO) Child Growth Standards, the head circumference for girls who are two-years old has a normal probability distribution witha mean of 47.2cm and a standard deviation of 1.4cm. What is the head circumference of a two-year old girl who marks the start of the 90th percentile? Enter a number without units.

Answer 1

Hence, 49.0 cm is the head circumference of a two-year old girl who marks the start of the 90th percentile.

Explanation:

We are given the following information in the question:

Mean, μ = 47.2 cm

Standard Deviation, σ = 1.4 cm

We are given that the distribution of head circumference is a bell shaped distribution that is a normal distribution.

Formula:

`z_(score) = \displaystyle(x-\mu)/(\sigma)`

We have to find the value of x such that the probability is 0.9

P(X < x)

`P( X < x) = P( z < \displaystyle(x - 47.2)/(1.4))=0.9`

`=P( z \leq \displaystyle(x - 47.2)/(1.4))=0.9`

Calculation the value from standard normal z table, we have,

`P(z \leq 1.282) = 0.90`

`\displaystyle(x - 47.2)/(1.4) = 1.282\\\\x = 48.9948 \approx 49.0`

Hence, 49.0 cm is the head circumference of a two-year old girl who marks the start of the 90th percentile.