# Statistical Measurements, Analysis and Research

## Homework 6 – Stats

- The tensile strength of a certain type of wire is normally distributed with a P of 99.8 and a
*σ*of 5.48.- What are the P and
*σ*of the sampling distribution of a sample mean (𝑥̅) based on simple random samples of size 100? - You draw a single random sample of 16 values from this population. What is the probability that the mean of this sample will be between 98.8 and 100.9?

- What are the P and
- A corporation employs 1,500 people. During the year the mean amount contributed to a charity drive per employee was $25.75. The standard deviation was $5.25. What is the probability that a simple random sample of 100 employees yields a mean between $25.00 and $27.00?
- In a population of sales people, the mean length of employment with their present firm is 2.5 years. The standard deviation is 3 years. A simple random sample of 40 is drawn from the population. What is the probability that the mean will be more than 3.5 years?
- A population has a P and
*σ*of 32 and 144, respectively. Consider the sampling distribution of 𝑥̅ based on simple random samples of size 64.^{2}- What are the mean and standard deviation of the sampling distribution?
- What proportion of the sample means is between 30 and 35?
- What is the probability that the mean of a single sample is greater than 35?
- What is the probability that the mean of a single sample is less than 30?

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