Math Answers

A manufacturer of a flu vaccine is concerned about the quality of its flu serum. Batches of serum are processed by three different departments having rejection rates of 0.20, 0.08, and 0.21, respectively. The inspections by the three departments are sequential and independent.

(a) What is the probability that a batch of serum survives the first departmental inspection but is rejected by the second department?

(b) What is the probability that a batch of serum is rejected by the third department?

A manufacturer of a flu vaccine is concerned about the quality of its flu serum. Batches of serum are processed by three different departments having rejection rates of 0.20, 0.08, and 0.12, respectively. The inspections by the three departments are sequential and independent.

(a) What is the probability that a batch of serum survives the first two departmental inspection but is rejected by the third department?

(b) What is the probability that a batch of serum is rejected by the first department?

A manufacturing firm employs three analytical plans for the design and development of a particular product. For cost reasons, all three are used at varying times. In fact, plans 1, 2, and 3 are used for 40%,, 15%, and 45% of the products respectively. The "defect rate:" is different for the three procedures as follows:

P(D\P1)=0.01, P{D\P2) = 0.03. P(D|P3 ) = 0.02,

where P(D\Pi) is the probability of a, defective product, given plan i. If a random product was observed and found to be defective, which plan was most likely used and thus responsible?

Suppose a car rental firm wants to estimate the average number of kilometers traveled per day by each of its cars rented in a certain city. A random sample of 20 cars rented in that city reveals that the sample mean travel distance per day is 85.5 kilometers, with a population standard deviation of 19.3 kilometers. Compute a 99% confidence interval to estimate Q. (2 points) Interpret your answer. (1 point)​

If F(x) 1/39(3x-2)2;0<_x_<3

O: elsewhere

1. Verify that F(x) is a PDF

2. find E(x) and Var(x)

Convert ((1−i)/2) into trigonometric form.

If z=8(cos5π3+isin5π3), then z6 is equal to

The amount of coffee dispensed by a vending machine is assumed to be normally distributed, A vendor claims that the mean amount of coffer dispensed by the machine is 6 ounces per cup. The office manager doubted this claim. He randomly selected 25 cups of coffee from this machine and recorded the amount of coffee dispensed in each. The sample mean is 5.8 ounces with a standard deviation of 0.8 ounces, do the data provide sufficient evidence to indicate that the mean amount of coffee dispensed is not equal to 6 ounces per cup use 0.05 level of significance.

2. A sample of 40 sales receipts from a grocery store has sample mean of 137 and population sd= 30.2. Use these values to test whether or not the mean sales the grocery store is less than 150. Use a 95% confidence level

The shelf life of a particular dairy product is normally distributed with a mean of 12 days and a standard deviation of 3 days. About what percent of the products last between 9 and 12 days?