Statistical Measurements, Analysis and Research

Homework 6 – Stats

1. The tensile strength of a certain type of wire is normally distributed with a P of 99.8 and a σ of 5.48.
   1. What are the P and σ of the sampling distribution of a sample mean (𝑥̅) based on simple random samples of size 100?
   2. 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?
2. 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?
3. 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?
4. A population has a P and σ² of 32 and 144, respectively. Consider the sampling distribution of 𝑥̅ based on simple random samples of size 64.
   1. What are the mean and standard deviation of the sampling distribution?
   2. What proportion of the sample means is between 30 and 35?
   3. What is the probability that the mean of a single sample is greater than 35?
   4. What is the probability that the mean of a single sample is less than 30?