Question

Suppose that it is known that the number of items produced in a factory during a week is a random variable with mean 50.

If the variance of a weekâs production is known to equal 26, then what can be said about the probability that this weekâs production will be between 40 and 60?

Answer 1

Solution :

Given that,

mean = = 50

variance = ² = 26

standard deviation = = 5.0990

P (40 < x < 60 )

P ( 40 - 50 / 5.0990) < ( x -  / ) < ( 60 - 50 / 5.0990)

P ( - 10 / 5.0990< z < 10 / 5.0990 )

P (-1.96 < z < 1.96 )

P ( z < 1.96 ) - P ( z < -1.96)

Using z table

= 0.9750 - 0.0250

= 0.9500

Probability = 0.9500