Q1:Suppose that the time it takes a data collection operator to fill out an electronic form for a database is uniformly between 1.5 and 2.2 minutes

(a) What are the mean and variance of the time it takes an operator to fill out the form?

(b) What is the probability that it will take less than two minutes to fill out the form?

(c) Determine the cumulative distribution function of the time it takes to fill out the form.

Q2) Assume that Z has a standard normal distribution. Usestandard normal distribution Table in theAppendixAto determine the value for z thatsolves each of the following:

Q3:The manufacturing of semiconductor chips produces 2% defective chips. Assume that the chips are independent and that a lot contains 1000 chips. Approximate the following probabilities

(a) More than 25 chips are defective.

(b) Between(at least)20 and(at most)30 chips are defective.

Q4:Suppose that the time to failure (in hours) of fans in a personal computer can be modeled by an exponential distribution with = 0.0003 :

(a) What proportion of the fans will last at least 10,000 hours?

(b) What proportion of the fans will last at most 7000 hours?

Q5:A driver's reaction time to visual stimulus is normally distributed with a mean of 0.4 seconds and a standard deviation of 0.05 seconds.What is the probability that a reaction requires more than 0.5 seconds?