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

Answer:

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

Step-by-step 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:

$z_{score} = \displaystyle\frac{x-\mu}{\sigma}$

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

P(X < x)  

$P( X < x) = P( z < \displaystyle\frac{x - 47.2}{1.4})=0.9$  

$=P( z \leq \displaystyle\frac{x - 47.2}{1.4})=0.9$  

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

$P(z \leq 1.282) = 0.90$

$\displaystyle\frac{x - 47.2}{1.4} = 1.282\\\\x = 48.9948 \approx 49.0$  

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