Answer to Question #158265 in Statistics and Probability for Eugine Haweza

Question

At the ministry of Health headquaters, you are in charge of rationing Southern province the area affected by hunger.

The following reports about daily calorier value of food available per adult during current period arrive from your local investigators. The estimated requirement of an adult is taken at 3000 calories per day and the absolute minimum at 1250. Advise the ministry by commenting on the reported figures and determine which in your own opinion needs more urgent attention

Areas of Kaoma

Gwembe with the Mean of 2580 and Standard deviation of 700.

Namwala with the Mean of 2300 and Standard deviation of 500.

Answer 1

We assume that the distributions of daily calorier value of food available per adult in both regions are normal with the parameters $(\mu_1,\sigma_1) = (2580, 700)$ and $(\mu_2,\sigma_2) = (2300, 500).$

Let X₁ and X₂ be random variables displaying the daily calorier value of food available per random adult in Gwembe and Namwala correspondently.

$P(X_1<3000) = \Phi(\frac{3000 - \mu_1}{\sigma_1}) = \Phi(\frac{3000-2580}{700}) = \Phi(0.6) = 0.7257$,

where $\Phi(x)=\frac{1}{\sqrt{2\pi}}\int\limits_{-\infty}^{x}e^{-x^2/2}dx$

$\Phi(x)=\frac{1}{\sqrt{2\pi}}\int\limits_{-\infty}^{x}e^{-x^2/2}dx$ is the standard cumulative distribution function (CDF).

$P(X_1<1250) = \Phi(\frac{1250 - \mu_1}{\sigma_1}) = \Phi(\frac{1250-2580}{700}) = \Phi(-1.9) = 0.0287$

$P(1250<X_1<3000) = 0.7257 - 0.0287 = 0.6977$

Similarly,

$P(X_2<3000) = \Phi(\frac{3000 - \mu_2}{\sigma_2}) = \Phi(\frac{3000-2300}{500}) = \Phi(1.4) = 0.9192$

$P(X_2<1250) = \Phi(\frac{1250 - \mu_2}{\sigma_2}) = \Phi(\frac{1250-2300}{500}) = \Phi(-2.1) = 0.0179$

$P(1250<X_2<3000) = 0.9192 - 0.0179 = 0.9013$

Comparing the situation in these two regions we obtain that in Namwala 91.92% of adult population receive food less than their estimated requirement, and in Gwembe - 72.57%.

But in Namwala there are 1.79% of adult population receive food less than the absolute minimum, whereas in Gwembe - 2.87%.

The advice to Ministry of Health: both regions extremely need humanitarian assistance, but Namwala is especially important of them.