Math Problem Statement
Smartphones: A poll agency reports that 48% of teenagers aged 12-17 own smartphones. A random sample of 150 teenagers is drawn. Round your answers to four decimal places as needed. (e) Find the probability that less than 55% of sampled teenagers own smartphones.
Solution
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Math Problem Analysis
Mathematical Concepts
Probability
Sampling Distribution
Normal Approximation to the Binomial Distribution
Formulas
Mean of sampling distribution \( \mu_{\hat{p}} = p \)
Standard deviation of sampling distribution \( \sigma_{\hat{p}} = \sqrt{\frac{p(1 - p)}{n}} \)
Z-score formula \( z = \frac{\hat{p} - \mu_{\hat{p}}}{\sigma_{\hat{p}}} \)
Theorems
Central Limit Theorem
Suitable Grade Level
Grades 10-12
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