Birth weight can be used to predict short and long-term health complications for babies. Studies sho

Question

Birth weight can be used to predict short and long-term health complications for babies. Studies show that the birth weight of babies born to mothers who do not smoke in a certain hospital can be assumed to follow a normal distribution with mean $3.05$ kg and variance ${{\sigma }^{2}}$kg$^{2}$.

The hospital classifies babies based on their birth weight as shown as in the table below.

Birth weight	Classification
Less than $1.5$ kg	Very low birth weight
$1.5$ kg to $2.5$ kg	Low birth weight
$2.5$ kg to $4.0$ kg	Normal birth weight
More than $4.0$ kg	High birth weight

A sample showed that $20.2%$ of the babies born to mothers who do not smoke have low birth weight. If this is true for the entire population, find two possible values of $\sigma $, corrected to $2$ decimal places. Explain clearly why one of the values of $\sigma $ found should be rejected.[4]

Accepted Answer

$\sigma = 0.70$ (2 d.p.); $\sigma = 1.56$ rejected

2019 ASRJC P2 Q6

2019 ASRJC P2 Q6

Video Solution:

Default solution

Birth weight	Classification
Less than \(1.5\) kg	Very low birth weight
\(1.5\) kg to \(2.5\) kg	Low birth weight
\(2.5\) kg to \(4.0\) kg	Normal birth weight
More than \(4.0\) kg	High birth weight