Smartphones: A poll agency reports that 32% of teenagers aged 12-17 own smartphones. A random sample of 100 teenagers is drawn. Round your answers to at least four decimal places as needed. (d) Find the probability that the proportion of the sampled teenagers who own a smartphone is between 0.29 and 0.35. The probability that the proportion of the sampled teenagers who own a smartphone is between 0.29 and 0.35 is?
Solution
_{} = [p ( 1 - p ) / n] = [(0.32 * 0.68) / 100] = 0.04666
= P[(0.29 - 0.32) / 0.04666 < ( - _{} ) / _{} < (0.35 - 0.32) / 0.04666]
= P(-0.643 < z < 0.643)
= P(z < 0.643) - P(z < -0.643)
= 0.4798
Probability = 0.4798
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