Question

The cholesterol level of children is normally distributed.

If the average cholesterol level is 194 with a standard deviation of 15, what percentage of children have a cholesterol level lower than 199? Answers are rounded to the nearest whole percent.

• a.)

  63%

• b.)

  74%

• c.)

  37%

• d.)

  26%

Answer 1

Let \(X\) be the cholestrol level.

\(X \sim N\left(\mu, \sigma^{2}\right)\)

where \(\mu=194\) and \(\sigma=15\)

Let \(Z=\frac{X-\mu}{\sigma} ; Z \sim N(0,1)\)

\(P(X \leq 199)\)

\(=P\left(\frac{X-\mu}{\sigma} \leq \frac{199-194}{15}\right)\)

\(=P(Z \leq 0.33)\)

\(=\Phi(0.33)\)

\(=0.63\)

ANS: a) \(63 \%\)