Slader records show that the average life expectancy of a pair of shoes is 2.2 years with astandard deviation of 1.7 years. A manufacturer gaurantees that shoes lasting less than a year are replaced for free. For every 1000 pairs sold how many pairs should the manufacturer expect to replaces free? Assume a normal distributiom.

Answer:For every 1000 pairs sold, the manufacturer expect to replace 239 pairs for free.Step-by-step explanation:Given:Mean (μ) = 2.2, Standard deviation(S.D) (σ) = 1.7 years and x = 1 (1 year)Let's find the Z score.Z = [tex]\frac{x - mean}{S.D}[/tex]Now plug in the given values in the above formula, we getZ = [tex]\frac{1 - 2.2}{1.7} = -0.71[/tex]Now we have to use the z-score table. The z-score for 0.71 is 0.2611Since it z is negative, so we subtract 0.2611 from 0.50000.5000 - 0.2611 = 0.2389Percentage = 0.2389 × 100 = 23.89%To find replaces for 1000 pairs, we need to multiply 23.89% by 1000= [tex]\frac{23.89}{100} .1000 = 238.9[/tex]= 239The cannot be in decimal, when we round off to the nearest whole, we get239