The distribution of the demand (in number of units per unit time) for a product

Question

The distribution of the demand (in number of units per unit time) for a product can often be approximated by a normal probability distribution. For example, a communication cable company has determined that the number of push-button terminal switches demanded daily has a normal distribution with mean 200 and standard deviation 50. a. On what percentage of days will the demand be less than 90 switches? b. On what percentage of days will the demand fall between 225 and 275 switches? c. Based on cost considerations, the company has determined that its best strategy is to produce a sufficient number of switches so that it will fully supply demand on 94% of all days. How many terminal switches should the company produce per day?

Explanation / Answer

Using z-table,

z value for 94 percentile is 1.555.

Hence

Number of switches = Mean +z value *SD

=200 + 1.555 *50

=277.75

=278

Answer will be 278 switches

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