Question

The weights of bags of baby carrots are normally distributed, with a mean of 35 ounces and a standard deviation of 0.29 ounce. Bags in the upper 4.5% are too heavy and must be repackaged. What is the most a bag of baby carrots can weigh and not need to be repackaged?

Answer 1

given,

mean weight of bag (μ) = 35

standard deviation (σ) = 0.29

percentage of bag heavier = 4.5%

weight of the bag less than 4.5 % = 100 - 4.5 = 95.5%

z- value according to 95.5% or 0.955 = 1.70

now, using formula:

Z = (x - μ)/σ

1.70 = (x - 35)/0.29

x - 35 = (1.70)(0.29)

x - 35 = 0.493

x = 0.49 + 35

x = 35.493