Tesla wanted to determine the average miles per kWh that their vehicles get across all models and variations. They took a sample

Question

2 months ago

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Tesla wanted to determine the average miles per kWh that their vehicles get across all models and variations. They took a sample

of 100 of their vehicles and recorded the resulting data. Assume that the true population mean is 30 kWh and that the population standard deviation is 3. Determine the correct mean and standard deviation for the sampling distribution of the sample mean__________ The mean is and the standard deviation is __________

Mathematics

1 answer:

lawyer [12.5K] · Answer 1 · 2026-03-17T22:33:06+03:00

Answer:

$\mu_{\bar x} = \mu = E(X) =30KWh$

$\sigma_{\bar X}= \frac{\sigma}{\sqrt{n}}=\frac{3}{\sqrt{100}}=0.3$

Step-by-step explanation:

Previous concepts

Normal distribution, is defined as a symmetric "probability distribution centered around the mean, indicating that values near the mean are more common than those further away".

The Z-score measures a value's relation to the mean of a set of values, displayed in terms of how many standard deviations away it is from that mean.

According to the central limit theorem, "with a population having mean μ and standard deviation σ, if we draw sufficient random samples from this population with replacement, the means of those samples will resemble a normal distribution, regardless of the original population's shape, as long as the sample size is large enough".

Solution to the problem

In this scenario, we select a sample size of n = 100

The central limit theorem informs us that the distribution of the sample mean $\bar X$ is defined by:

$\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})$

Thus, the mean for the sample would be:

$\mu_{\bar x} = \mu = E(X) =30KWh$

And the standard deviation would be:

$\sigma_{\bar X}= \frac{\sigma}{\sqrt{n}}=\frac{3}{\sqrt{100}}=0.3$