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3 years ago

7

The value of an antique car is modeled by the function v(x)=107,000(1.009)^(2/3x) where x is the number of years since 2005. by

what approximate percent rate is the value of the car increasing per year?

1 answer:

baherus [9]3 years ago

8 0

You would multiply the growth rate (.009) by 2/3 to get the percent rate per year. Therefore, the answer is .006

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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:

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

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

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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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