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Let \( X \) represent the full height of a certain species of tree. Assume that \( X \) has a normal probability distribution with \(\mu = 151.5 \, \text{ft}\) and \(\sigma = 97.7 \, \text{ft}\). You intend to measure a random sample of \( n = 226 \) trees.

1. What is the mean of the distribution of sample means?
\[ \mu_{\bar{x}} = \]

2. What is the standard deviation of the distribution of sample means (i.e., the standard error in estimating the mean)?
\[ \sigma_{\bar{x}} = \]

Report your answers rounded to 4 decimal places.

Answer :

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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Rewritten by : Barada

The sample mean is equal to the X mean, µ = 151.5.

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

What is the formula for the probability distribution?

Probability distribution function

F (x) = P (X ≤ x) can be written. If there is also a semi-closed interval given by (a, b], the probability distribution function is given by the equation P (a ≤ b) = F (b) -F (a). Always between 0 and 1.

What is the probability distribution and its type?

There are two types of probability distributions used for different purposes and different types of data generation processes.

  1. Normal or cumulative probability distribution.
  2. Binary or discrete probability distribution.

Learn more about probability distribution here: https://brainly.com/question/24756209

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