SOLUTION: The weight of a small Starbucks coffee is a normally distributed random variable with a mean of 395 grams and a standard deviation of 22 grams. Find the weight that corresponds to

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Question 1152486: The weight of a small Starbucks coffee is a normally distributed random variable with a mean of 395 grams and a standard deviation of 22 grams. Find the weight that corresponds to each event. (Use Excel or Appendix C to calculate the z-value. Round your final answers to 2 decimal places.)

a. Highest 30 percent

b. Middle 70 percent to (2 answers)
c. Highest 90 percent

d. Lowest 20 percent

Answer by Boreal(15235) (Show Source):
You can put this solution on YOUR website!
For 70th percentile or highest 30 per cent z=0.52
z=(x-mean)/sd
0.5244=(x-395)/22
11.54=x-395
x=406.54 gm
middle 70% is from 15 to 85 per cent. Use symmetry and figure 1
z.15 is -1.036
-22.80=x-395
x=372.20 gm
the other value, the 85th percentile, is 395+22.80=417.80 gm. That is range.
highest 90% is z=1.282
28.20=(x-mean)
x=423.20
Lowest 20% is -0.8416=z
-18.52=x-395
x=376.48 gm