Sixteen percent of the world\'s population is left-handed. A researcher claims t

Question

Sixteen percent of the world's population is left-handed. A researcher claims that left-handed individuals are more creative than those who aren't left-handed. In order to support his claim, he takes a sample of 2100 artists and finds that 14% of them are left-handed. a. Find the mean of p, where p is the proportion of left-handed individuals in a random sample of 2100. b. Find the standard deviation of p. c. Compute an approximation for P (p lessthanorequalto 0.14), which is the probability that there will be 14% or fewer left-handed people in a random sample of 2100. Round your answer to four decimal places.

Explanation / Answer

a) mean (p) = 0.16 , q = 1 - 0.16 = 0.84 , n =2100

b) Standard deviation = sqrt[ ( p * q) / n ]

= sqrt [ ( 0.16 * 0.84) / 2100]

= 0.008

c) z = ( 0.14 - 0.16) / 0.008 = -2.5

P( Z < -2.5) = .0062

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