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Alekssandra [29.7K]
2 years ago
6

Let X represent the full height of a certain species of tree. Assume that X has a normal probability distribution with μ = 151.5

ft and σ = 97.7 ft. You intend to measure a random sample of n = 226 trees.
What is the mean of the distribution of sample means?
μ¯x =

What is the standard deviation of the distribution of sample means (i.e., the standard error in estimating the mean)?
σ¯x =

Report your answers rounded to 4 decimal places.
Mathematics
1 answer:
viva [34]2 years ago
5 0

The mean of the random samples is the same as the mean of X, µ = 151.5.

The standard error is the standard deviation of X divided by the square root of the sample size, σ = 97.7/√226 ≈ 6.6320.

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Answer:

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Step-by-step explanation:

In the division statement: m ÷ n = q + \frac{r}{n}

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Let us use the fact above to solve the question

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→ Multiply the 2 brackets at first

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∴ (x² - x + 2)(2x - 3) = 2x³ - 3x² - 2x² + 3x + 4x - 6

→ Add the like terms

∴ (x² - x + 2)(2x - 3) = 2x³ + (-3x² - 2x²) + (3x + 4x) - 6

∴ (x² - x + 2)(2x - 3) = 2x³ + (-5x²) + 7x - 6

∴ (x² - x + 2)(2x - 3) = 2x³ - 5x² + 7x - 6

→ Substitute it in f(x)

∴ f(x) = 2x³ - 5x² + 7x - 6 - 1

→ Add the like term

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∴ f(x) = 2x³ - 5x² + 7x + (-7)

∴ f(x) = 2x³ - 5x² + 7x - 7

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