Records kept by the chief dietitian at the university cafeteria over a 29-week period show the following weekly consumption of milk (in gallons):| Milk (gallons) | 200 | 205 | 210 | 215 | 220 | 225 | 230 | 235 | 240 ||----------------|-----|-----|-----|-----|-----|-----|-----|-----|-----|| Weeks | 5 | 3 | 6 | 2 | 3 | 5 | 2 | 2 | 1 |**(a)** Find the average number of gallons of milk consumed per week in the cafeteria. (Round your answer to the nearest whole number.)\[ \_\_\_\_\_ \text{ gal} \]**(b)** Let the random variable $ X $ denote the number of gallons of milk consumed in a week at the cafeteria. Find the probability distribution of the random variable $ X $. (Round your answers to three decimal places.)| Milk (gallons) | 200 | 205 | 210 | 215 | 220 | 225 | 230 | 235 | 240 ||----------------|-------|-------|-------|-------|-------|-------|-------|-------|-------|| $ P(X = x) $ | \_\_\_\_ | \_\_\_\_ | \_\_\_\_ | \_\_\_\_ | \_\_\_\_ | \_\_\_\_ | \_\_\_\_ | \_\_\_\_ | \_\_\_\_ |Compute $ E(X) $, the expected value of $ X $. (Round your answer to the nearest whole number.)\[ E(X) = \_\_\_\_\_ \text{ gal} \]

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A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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