Answered: **T6.11.** Let $ Y $ denote the…

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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$**T6.11.** Let $ Y $ denote the number of broken eggs in a randomly selected carton of one dozen "store brand" eggs at a local supermarket. Suppose that the probability distribution of $ Y $ is as follows. \[ \begin{array}{|c|c|c|c|c|c|} \hline \text{Value } y_i & 0 & 1 & 2 & 3 & 4 \\ \hline \text{Probability } p_i & 0.78 & 0.11 & 0.07 & 0.03 & 0.01 \\ \hline \end{array} \] (a) What is the probability that at least 10 eggs in a randomly selected carton are **unbroken**? (b) Calculate and interpret $ \mu_Y $. (c) Calculate $ \sigma_Y $. Show your work. (d) A quality control inspector at the store keeps looking at randomly selected cartons of eggs until he finds one with at least 2 broken eggs. Find the probability that this happens in one of the first three cartons he inspects.$

Transcribed Image Text:**T6.11.** Let $ Y $ denote the number of broken eggs in a randomly selected carton of one dozen "store brand" eggs at a local supermarket. Suppose that the probability distribution of $ Y $ is as follows. \[ \begin{array}{|c|c|c|c|c|c|} \hline \text{Value } y_i & 0 & 1 & 2 & 3 & 4 \\ \hline \text{Probability } p_i & 0.78 & 0.11 & 0.07 & 0.03 & 0.01 \\ \hline \end{array} \] (a) What is the probability that at least 10 eggs in a randomly selected carton are **unbroken**? (b) Calculate and interpret $ \mu_Y $. (c) Calculate $ \sigma_Y $. Show your work. (d) A quality control inspector at the store keeps looking at randomly selected cartons of eggs until he finds one with at least 2 broken eggs. Find the probability that this happens in one of the first three cartons he inspects.

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