A survey of 2, 350 adults reported that 56% watch news videos. Complete parts (a
ID: 3264526 • Letter: A
Question
A survey of 2, 350 adults reported that 56% watch news videos. Complete parts (a) through (c) below. a. Suppose that you take a sample of 100 adults. If the population proportion of adults who watch news videos is 0.56, what is the probability that fewer than half in your sample will watch news videos? The probability is 0.1133 that fewer than half of the adults in the sample will watch news videos. b. Suppose that you take a sample of 500 adults. If the population proportion of adults who watch news videos is 0.56, what is the probability that fewer than half in your sample will watch news videos? The probability is that fewer than half of the adults in the sample will watch news videos.Explanation / Answer
p = 0.5 , p0 = 0.56
a)
p( p < 0.5) = p( z < 0.5 - 0.56 / Sqrt(0.56*0.44/100)
= p ( z < -0.06 / 0.04964)
= p( z < -1.209)
= 1 - p( z < 1.2087)
= 1 - 0.88667
= 0.1133
b)
p(p < 0.5) = p(z < 0.5 - 0.56 / Sqrt(0.56*0.44/500)
= p(z < -0.06 / 0.0222)
= p(z< -2.703)
= 1 - p( z < 2.703)
= 1 - 0.99656
= 0.0034
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