Question

Suppose that the monthly demand for a consumer good follows a normal distribution with a deviation of 94 kg.

We know that the probability of monthly demand is below 502 kg. is 0.12.

Find the mean of the distribution.

Answer 1

Suppose that the monthly demand for a consumer good follows a normal distribution with a standard deviation of 94 kgs.

Let, the mean of the distribution be m.

We know that the probability that the monthly demand is below 502 kgs, is 0.12.

We have to find the value of m.

Now, if X be the random variable denoting the demand for a randomly selected month, then X follows normal with mean m and standard deviation of 94.

So, we can say that

Z=(X-m)/94 follows standard normal with mean 0 and standard deviation 1.

So, we have

Where, phi is the CDF of the standard normal variate.

Now, from standard normal table, we know that

So, comparing, we get

So, the mean monthly demand is 612.45 kgs.