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Readme [11.4K]
2 years ago
11

A study by Allstate Insurance Co. finds that 82% of teenagers have used cell phones while driving (the Wall Street Journal, May

5, 2010). Suppose a random sample of 100 teen drivers is taken. What is the probability that the sample proportion is within ± 0.02 of the population proportion?
Mathematics
1 answer:
Strike441 [17]2 years ago
4 0

The probability that the sample proportion is within ± 0.02 of the population proportion is 0.3328

<h3>How to determine the probability?</h3>

The given parameters are:

  • Sample size, n = 100
  • Population proportion, p = 82%

Start by calculating the mean:

\mu = np

\mu = 100 * 82\%

\mu = 82

Calculate the standard deviation:

\sigma = \sqrt{\mu(1 - p)

\sigma = \sqrt{82 * (1 - 82\%)

\sigma = 3.84

Within ± 0.02 of the population proportion are:

x_{min} = 82 * (1 - 0.02) = 80.38

x_{max} = 82 * (1 + 0.02) = 83.64

Calculate the z-scores at these points using:

z = \frac{x - \mu}{\sigma}

So, we have:

z_1 = \frac{80.36 - 82}{3.84} = -0.43

z_2 = \frac{83.64 - 82}{3.84} = 0.43

The probability is then represented as:

P(x ± 0.02) = P(-0.43 < z < 0.43)

Using the z table of probabilities, we have:

P(x ± 0.02) = 0.3328

Hence, the probability that the sample proportion is within ± 0.02 of the population proportion is 0.3328

Read more about probability at:

brainly.com/question/25870256

#SPJ1

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