Strater, Inc. makes particleboard for the building industry. Particleboard is made by mixing wood chips and resins together, forming the mix into 4 foot by 8 foot sheets, and pressing the sheets under extreme heat and pressure to form a sheet that is used as a substitute for plywood. The strength of the particleboard is tied to the board's weight. Boards that are too light are brittle and do not meet the quality standard for strength. Boards that are too heavy are strong but are difficult for the customers to work with. The company knows that there will be variation in the boards' weight. Product specifications call for the weight per sheet to average 10 pounds with a standard deviation of 1.75 pounds. During each shift, Strater employees select and weigh a random sample of 25 boards. The boards are thought to have a normally distributed weight distribution.

If the average of the sample slips below 9.60 pounds, and adjustment is made to the process to add more moisture and resin to increase the weight (and hopefully the strength).

1. Assuming that the process is operating correctly according to specifications, what is the probability that a sample will indicate that an adjustment is needed?

2. Assume the population mean weight per sheet slips to 9 pounds. Determine the probability that the sample will indicate that an adjustment is not needed.

3. Assuming that 10 pounds is the mean weight, what should the cutoff be if the company wants no more than 5% chance that a sample of 25 boards will have an average weight less than 9.6 lbs?

Solution Summary

This solution uses the sampling distribution of the sample mean and normal probability distributions to solve the three parts of this question.

Which of the following is true about thesamplingdistribution of thesamplemean?
A. Themean of thesamplingdistribution is always "u"
B. The standard deviation of thesamplingdistribution is always "o"
C. The shape of thesamplingdistribution is always approximately normal
D. All of the above

In a manufacturing process a machine produces bolts that have an average length of 3 inches with a variance of .03. If we randomly select three bolts from this process: What is the standard deviation of thesamplingdistribution of thesamplemean?

Suppose the annual consumption of chicken mean is 20.84 pounds per person, and that the standard deviation for the consumption of chicken per person is 9.193 pounds. Themean weight of chicken consumed for a sample of 200 randomly selected people is one value of many that form thesamplingdistribution of samplemeans.
Descri

For a sample size 16, thesamplingdistribution of themean will be approximately normally distributed:
A. regardless of the shape of the population
B. if the shape of the population is symmetrical
C. if thesample standard deviation is known
D. if thesample is normally distributed

Suppose the annual consumption of chicken mean is 20.84 pounds per person and that the standard deviation for the consumption of chicken per person is 9.193 pounds. Themean weight of chicken consumed for a sample of 200 randomly selected people is one value of many that form thesamplingdistribution of samplemeans.
Descri

What is thesamplingdistribution of samplemeans?
What is themean of thesamplingdistribution of samplemeans?
What is its standard deviation?
How is that standard deviation affected by thesample size?
What does the central limit theorem state about that distribution?

6.30
Given a population in which the proportion of items with a desired attribute is p=0.25, if a sample of 400 is taken:
a. What is the standard deviation of thesamplingdistribution of _
P?
b. What is the probability the propo

Please answer and fully explain the below question:
Under what condition, if any, is it not possible for us to assume that thesamplingdistribution of thesamplemean is approximately normally distributed?

Suppose Stat I students ages follow a skewed right distribution with a mean of 24 years old and a standard deviation of 2 years old. If we randomly sampled 150 students, which of the following statements about thesamplingdistribution of thesamplemean age is incorrect?
-Themean of thesamplingdistribution is approximate

Last year, a national opinion poll found that 43% of all Americans agree that parents should be given vouchers good for education at any public or private school of their choice. Assume that in fact the population proportion is 0.43. A random sample of 350 is to be selected and asked the same question.
a) What is the shape, m