Question

In a factory the daily average production is 146 units, with a standard deviation of 10 units, following an unknown distribution.

How much total production can we guarantee for 40 days with a 0.90 probability?

Probability statement used is .

The value from the table is .

The total production is  and the average daily production is .

Answer 1

Let X denote the daily production. It is given that X has mean u = 146 and standard deviation o=10 also we have number of days n= 40 40 Then Y = x has mean 40u = 5840 and standard deviation V400 = 63.2455 1-1 Now, let C denote the required production then. C-5840 P(Y>C)=0.90 = PZ> = 0.90 63.2455 Then from standard normal table we get C-5840 -=-1.2815 = C = 5840-(1.2815*63.2455) = 5758.948 63.2455 Normal Curve, mean = 0, SD = 1 Shaded Area = 0.9 04 03 02 0.1 0.0 -1.2815 0