(a) Explanation Given: Four candies are selected from a bag and the number of orange candies is recorded. Explanation: Consider a box that contains 20% orange candies. Four candies are selected from a bag and the number of orange candies is recorded. A success occurs if an orange candy is selected. So, the probability of success is P = 20 % = 1 5 Use the binomial probability P ( x successes in n trials ) = C ( n , x ) p x ( 1 − p ) n − x So, substitute n = 4 and P = 1 5 , the binomial probability is P ( x successes in 4 trials ) = C ( 4 , x ) ( 1 5 ) x ( 1 − 1 5 ) 4 − x = C ( 4 , x ) ( 1 5 ) x ( 4 5 ) 4 − x Assume that x represents the random variable “number of orange candies.” So, x can take on the values 0, 1, 2, 3, or 4. Substitute x = 0 P ( x = 0 ) = C ( 4 , 0 ) × ( 1 5 ) 0 × ( 4 5 ) 4 − 0 = 1 × 1 × ( 4 5 ) 4 = ( 0.8 ) 4 = 0.4096 Substitute x = 1 P ( x = 1 ) = C ( 4 , 1 ) × ( 1 5 ) 1 × ( 4 5 ) 4 − 1 = 4 × 1 5 × ( 4 5 ) 3 = ( 0 (b) To determine The histogram for the probability distribution if four candies are selected from a bag and the number of orange candies is recorded. (c) To determine The expected value if four candies are selected from a bag and the number of orange candies is recorded.

11th Edition

ISBN: 9780321979438

Author: Margaret L. Lial, Raymond N. Greenwell, Nathan P. Ritchey

Publisher: PEARSON

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Chapter 8, Problem 70RE

(a)

To determine

The probability distribution if four candies are selected from a bag and the number of orange candies is recorded.

(b)

To determine

The histogram for the probability distribution if four candies are selected from a bag and the number of orange candies is recorded.

(c)

To determine

The expected value if four candies are selected from a bag and the number of orange candies is recorded.

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Chapter 8, Problem 69RE

Chapter 8, Problem 71RE

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Chapter 8 Solutions

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The probability distribution if four candies are selected from a bag and the number of orange candies is recorded.

Solution Summary: The author explains how to determine the probability distribution if four candies are selected from a bag and the number of orange candy is recorded. The binomial probability is n=4and P=

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The probability distribution if four candies are selected from a bag and the number of orange candies is recorded.

The histogram for the probability distribution if four candies are selected from a bag and the number of orange candies is recorded.

The expected value if four candies are selected from a bag and the number of orange candies is recorded.

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