Answer: 0.375
Step-by-step explanation:
Given: The difference between actual and predicted weekly sales of a company follows a uniform distribution between -$4000 and $4000.
Probability density function: [tex]f(x)=\dfrac{1}{b-a}=\dfrac{1}{4000-(-4000)}=\dfrac{1}{8000}[/tex]
The probability that the actual sale is within $1500 of the predicted sale = [tex]\int^{1500}_{-1500}f(x)dx=\int^{1500}_{-1500}\dfrac{1}{8000}dx=\dfrac{1}{8000}[x]^{1500}_{-1500}\\\\= \dfrac{1}{8000}(1500-(-1500))\\\\= \dfrac{1}{8000}(3000)=0.375[/tex]
Hence, Required probability =0.375
