Question

A textile manufacturing company wants to study the rate of production for a merino wool blanket that is produced in one of their textile facilities. Past data reveals that the production of one batch of blankets has a mean of 36 days with standard deviation 10 days. The normal distribution for the population is shown by the dotted black line. The company plans to take a random sample of 32 such batches of blankets and will calculate the mean production period of the sample to compare to the known production periods. Compute the the mean and standard deviation of the sampling distribution of sample means for a sample of size 32. Round your answers to the nearest tenth. Show your answer by moving the two draggable points to build the sampling distribution.

Answer 1

The mean of the sampling distribution of sample means is 36 days, and the standard deviation, or standard error, is approximately 1.8 days.

Step-by-step explanation:

To compute the mean and standard deviation of the sampling distribution of sample means for a sample size of 32, the Central Limit Theorem is used. Since the population mean (μ) is 36 days and the population standard deviation (σ) is 10 days, for a sample size (n) of 32, the sampling distribution of the sample mean will have the following properties:

• The mean of the sampling distribution (μm) is equal to the population mean (μ), which is 36 days.
• The standard deviation of the sampling distribution (σm), also known as the standard error (SE), is equal to the population standard deviation (σ) divided by the square root of the sample size (n).

Therefore, σm = σ / √n = 10 / √32 ≈ 10 / 5.6569 ≈ 1.8 days (rounded to the nearest tenth).

The mean of the sampling distribution is 36 days, and the standard deviation is roughly 1.8 days.