Question

A machine fills sugar boxes in such a way that the weights (in grams) are normally distributed with a mean of 2260 g and a standard deviation of 20 g. Another machine checks the weights and rejects packages in the bottom 1% of weights and the top 1% of weights. Find the the minimum and maximum acceptable weights. Answer using whole numbers and enter the bottom 1% value in blank 1 and the top 1% in blank 2.

i know how to work the top 1% but unsure of the bottom 1%

Answer 1

Bottom 1% means less than upper 99% and 1% top means more than lower 99%

Using the z distribution table, we get for 99% level

So, z value for bottom 1% will be -2.33 because its below the mean and z score for top 1% will be 2.33 because it above mean.

using the formula

For bottom 1%, we have z value= -2.33,

we have to find the value of

setting the given values, we get

-2.33 = (-2260)/20

multiplying both sides by 20, we get

-2.33*20 = (-2260) on right hand side, 20/20 becomes 1

-46.6 = - 2260

adding 2260 on each side, we get

-46.6 + 2260 = - 2260+2260 on right hand side, -2260+2260 becomes 0

we get = 2260-46.6 = 2213.4 or 2213 (nearest whole number)

Similarly for top 1%,

we have z value= 2.33,

we have to find the value of

setting the given values, we get

2.33 = (-2260)/20

multiplying both sides by 20, we get

2.33*20 = (-2260) on right hand side, 20/20 becomes 1

46.6 = - 2260

adding 2260 on each side, we get

46.6 + 2260 = - 2260+2260 on right hand side, -2260+2260 becomes 0

we get = 2260+46.6 = 2306.6 or 2307 (nearest whole number)

So, bottom 1% value is 2213

top 1% value is 2307