Question

Suppose the difference between actual and predicted weekly sales of a company follows a uniform distribution between -$4000 and $4000. Determine the probability that the actual sale is within $1500 of the predicted sale (which means P(-1500

Answer 1

Answer: 0.375

Explanation:

Given: The difference between actual and predicted weekly sales of a company follows a uniform distribution between -$4000 and $4000.

Probability density function:
`f(x)=(1)/(b-a)=(1)/(4000-(-4000))=(1)/(8000)`

The probability that the actual sale is within $1500 of the predicted sale =
`\int^(1500)_(-1500)f(x)dx=\int^(1500)_(-1500)(1)/(8000)dx=(1)/(8000)[x]^(1500)_(-1500)\\\\= (1)/(8000)(1500-(-1500))\\\\= (1)/(8000)(3000)=0.375`

Hence, Required probability =0.375