(a) Explanation Given info: Let n be number of people at the town meeting = 350. Let p be the probability of residents in the town favor the construction of parking lot = 0.35. Let X denote the number of residents in the town favors the construction of parking lot and it follows the binomial distribution with parameters ( n = 150 , p = 0.053 ) . Calculation: Check the conditions for normal approximation: n p ≥ 5 350 ( 0.35 ) ≥ 5 122.5 ≥ 5 n ( 1 − p ) ≥ 5 350 ( 1 − 0.35 ) ≥ 5 227.5 ≥ 5 Hence, both the conditions are satisfied. The mean of the R.V ( X ) is, μ = n p = 350 ( 0.35 ) = 227.5 The standard deviation of the R.V ( X ) is, σ = n p ( 1 − p ) = 350 ( 0.35 ) ( 1 − 0.35 ) = 8.92 The probability that at least 100 favor construction of the parking lot is, P ( X ≥ 100 ) = P ( X > 100 − 0 (b) To determine To identify: Check whether it is likely that 100 or more people would favor the parking lot. To explain: The reason for likely that 100 or more people would favor the parking lot.

ELEMENTARY STATISTICS: STEP BY STEP- ALE

10th Edition

ISBN: 9781266422362

Author: Bluman

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Chapter 6.4, Problem 22E

(a)

To determine

To find: The probability that at least 100 favor construction of the parking lot.

(b)

To determine

To identify: Check whether it is likely that 100 or more people would favor the parking lot.

To explain: The reason for likely that 100 or more people would favor the parking lot.

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Chapter 6.4, Problem 21E

Chapter 6.4, Problem 23EC

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Chapter 6 Solutions

ELEMENTARY STATISTICS: STEP BY STEP- ALE

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The probability that at least 100 favor construction of the parking lot.

Solution Summary: The author explains that the probability that at least 100 favor construction of the parking lot is 0.7157.