Question

Assume that the number of defective basketballs produced is related by a linear equation to the total number produced. Suppose that 13 defective balls are produced in a lot of 250, and 19 defective balls are produced in a lot of 450.

Find the EXPECTED number of defective balls produced in a lot of 625 balls.

Answer 1

let x be the total number of balls in a lot and y be the number of defective balls

Then we have (x1,y1)= (250,13) and (x2,y2) =(450,19)

we know that the linear equation is represented as y = ax+b

where a is slope and b is intercept

we know the formula for slope (a) = (y2-y1)/(x2-x1)

setting the values, we get

slope(a) = (19-13)/(450-250) = 6/200 = 3/100 = 0.03

Now, using the slope(a) and point (x1,y1) to find the value of intercept, we get

13 = 0.03*250 + b

on solving, we get

13 = 7.5 + b

subtracting 7.5 on each side, we get

13-7.5 = b

or b = 5.5

So, the intercept is b= 5.5

thus, the required linear relationship is y = 0.03x + 5.5

Now, we have to find the expected number of defective balls produced in a lot of 625 balls

so setting x = 625 in the equation, we get

y = 0.03*625 + 5.5 = 18.75+5.5 = 24.25

So, expected number of defectiv balls is 24 (rounded to nearest whole number)