Question 1.1

A production process manufactures items with weights that are normally distributed with mean of 17 pounds and a standard deviation of 0.1 pounds. An item is considered to be defective if its weight is less than 16.85 pounds or greater than 17.15 pounds. Suppose that these items are currently produced in batches of 500 units.

1. Find the probability that an inspected item is defective.
2. Find the probability that at most 10% of the items in a given batch will be defective.
3. Find the probability that at least 90% of the items in a given batch will be acceptable.

Hint: Find the probability that an item is defective using Normal probabilities. Then, you can model a number of defectives out of 500 as Binomial. 1.2

Hits on a personal website occur quite infrequently. They occur randomly and independently with an average of five per week.

1. Find the probability that the site gets 10 or more hits in a week.
2. Determine the probability that the site gets 20 or more hits in 2 weeks. 1.3

An electronic switch has a constant failure rate of 10^-3per hour.

1. What is the expected life of the switch and What is the standard deviation of the switch also, What is the probability that the switch will last between 1200 and 1400 hours?

Hint: Model the lifetime of the switch as exponential distribution with = 10^-3per hour.