normal population has a mean of $84 and standard deviation of $14. You select random samples of 40. Apply the central limit theorem to describe the sampling distribution of the sample mean with n= 40. What condition is necessary ply the central limit theorem? Applying the central limit theorem requires the population distribution to be normal.

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I need help answering D and E please

A normal population has a mean of $84 and a standard deviation of $14. You select random samples of 40.

a. Apply the central limit theorem to describe the sampling distribution of the sample mean with n = 40. What condition is necessary to apply the central limit theorem?

- **Applying the central limit theorem requires the population distribution to be:** 
  - *Normal.*

b. What is the standard error of the sampling distribution of sample means? (Round your answer to 2 decimal places.)

- **Standard Error:**

c. What is the probability that a sample mean is less than $83? (Round z value to 2 decimal places and final answer to 4 decimal places)

- **Probability:**

d. What is the probability that a sample mean is between $83 and $85? (Round z value to 2 decimal places and final answer to 4 decimal places)

- **Probability:**

e. What is the probability that a sample mean is between $85 and $86? (Round z value to 2 decimal places and final answer to 4 decimal places)

- **Probability:**
Transcribed Image Text:A normal population has a mean of $84 and a standard deviation of $14. You select random samples of 40. a. Apply the central limit theorem to describe the sampling distribution of the sample mean with n = 40. What condition is necessary to apply the central limit theorem? - **Applying the central limit theorem requires the population distribution to be:** - *Normal.* b. What is the standard error of the sampling distribution of sample means? (Round your answer to 2 decimal places.) - **Standard Error:** c. What is the probability that a sample mean is less than $83? (Round z value to 2 decimal places and final answer to 4 decimal places) - **Probability:** d. What is the probability that a sample mean is between $83 and $85? (Round z value to 2 decimal places and final answer to 4 decimal places) - **Probability:** e. What is the probability that a sample mean is between $85 and $86? (Round z value to 2 decimal places and final answer to 4 decimal places) - **Probability:**
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