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Question 8. [This question is based, in part, on Example 2a, p. 431, in the textbook] Let the random variable X be the number of cans produced in a

Please solve to the best of your ability. Show steps so I can understand.Screen Shot 2018-04-29 at 4.32.05 PM.png

Screen Shot 2018-04-29 at 4.32.05 PM.png

Question 8. [This question is based, in part, on Example 2a, p. 431, in the textbook] Let the random variable X be the number of cans produced in a canning factory during a
randomly chosen one-week period. (a) If E (X) : 50 and Var(X) : 25 then what can be said about P(40 g X g 60)? [Hintz
Chebyshev’s inequality]
(b) Prove the Central Limit Theorem for a sequence of independent, identically distributed random variables X 1, X 2, . . . each having mean [1, and variance 02. (c) Let X1, . . . ,X100 be the number of cans produced by the factory in a random sample
of 100 weeks, and let X = (X1 + - - . + X100) / 100 denote the corresponding sample mean.
Show that P(49 g X S 51) 2’ 0.9544. [Note: Please ignore the usual continuity correction]

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