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**Normal Distribution Exercise: Small Starbucks Coffee** The weight of a small Starbucks coffee is a normally distributed random variable with a mean of 365 grams and a standard deviation of 14 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 10 percent: [Input Box] b. Middle 50 percent: [Input Box] to [Input Box] c. Highest 80 percent: [Input Box] d. Lowest 10 percent: [Input Box]

**Normal Distribution Exercise: Small Starbucks Coffee** The weight of a small Starbucks coffee is a normally distributed random variable with a mean of 365 grams and a standard deviation of 14 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 10 percent: [Input Box] b. Middle 50 percent: [Input Box] to [Input Box] c. Highest 80 percent: [Input Box] d. Lowest 10 percent: [Input Box]

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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**Normal Distribution Exercise: Small Starbucks Coffee** The weight of a small Starbucks coffee is a normally distributed random variable with a mean of 365 grams and a standard deviation of 14 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 10 percent: [Input Box] b. Middle 50 percent: [Input Box] to [Input Box] c. Highest 80 percent: [Input Box] d. Lowest 10 percent: [Input Box]
Transcribed Image Text:**Normal Distribution Exercise: Small Starbucks Coffee** The weight of a small Starbucks coffee is a normally distributed random variable with a mean of 365 grams and a standard deviation of 14 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 10 percent: [Input Box] b. Middle 50 percent: [Input Box] to [Input Box] c. Highest 80 percent: [Input Box] d. Lowest 10 percent: [Input Box]
Expert Solution
Step 1

Let X denote the weight of a small coffee. Then X~N(365, 142)

Part a: The value of X is such that

                   P(Z≥z)=0.10⇒ PZ≤z=0.90

 From the normal tables, we have

                 P(Z≤1.28)=0.90

        ⇒X-36514=1.28⇒         X = 382.92 

Part b: For the middle 50%, X is such that

                         P(-z≤Z≤z)=0.50⇒ P(|Z|≤z)=0.50

    From the normal tables we have

                        P(|Z|≤0.68)=0.50

                 ⇒ X-36514=±0.68⇒  X-36514=+0.68   &  X-36514=-0.68⇒            X=374.52   &           X=355.48

Hence the middle 50% lie between the values 355.48 and 374.52

 

         

             

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