# Question: Each day a manufacturing plant receives a large shipment of

Each day a manufacturing plant receives a large shipment of drums of Chemical ZX- 900. These drums are supposed to have a mean fill of 50 gallons, while the fills have a standard deviation known to be .6 gallon.

a. Suppose that the mean fill for the shipment is actually 50 gallons. If we draw a random sample of 100 drums from the shipment, what is the probability that the average fill for the 100 drums is between 49.88 gallons and 50.12 gallons?

b. The plant manager is worried that the drums of Chemical ZX- 900 are underfilled. Because of this, she decides to draw a sample of 100 drums from each daily shipment and will reject the shipment (send it back to the supplier) if the average fill for the 100 drums is less than 49.85 gallons. Suppose that a shipment that actually has a mean fill of 50 gallons is received. What is the probability that this shipment will be rejected and sent back to the supplier?

a. Suppose that the mean fill for the shipment is actually 50 gallons. If we draw a random sample of 100 drums from the shipment, what is the probability that the average fill for the 100 drums is between 49.88 gallons and 50.12 gallons?

b. The plant manager is worried that the drums of Chemical ZX- 900 are underfilled. Because of this, she decides to draw a sample of 100 drums from each daily shipment and will reject the shipment (send it back to the supplier) if the average fill for the 100 drums is less than 49.85 gallons. Suppose that a shipment that actually has a mean fill of 50 gallons is received. What is the probability that this shipment will be rejected and sent back to the supplier?

## Answer to relevant Questions

Suppose that we will take a random sample of size n from a population having mean µ and standard deviation s. For each of the following situations, find the mean, variance, and standard deviation of the sampling ...Find the probability distribution of the population of six sample mean grand prizes. In each of the following cases, determine whether the sample size n is large enough to say that the sampling distribution of p is a normal distribution. a. p = .4, n = 100 b. p =.1, n =10 c. p =.1, n =50 d. p =.8, n= 400 ...Based on your results in Exercise 7.30, would it be reasonable to state that the survey’s “margin of error” is +-3 percentage points? + - 6 percentage points? Explain. Explain how each of the following changes as the number of degrees of freedom describing a t curve increases: a. The standard deviation of the t curve. b. The points tα and tα/2.Post your question