The bulbs manufactured by a company gave a mean life of 3000 hours with standard deviation of 400 hours. If a bulb is selected at random, what is the probability it will have a mean life less than 2000 hours?

Question:

1) Calculate the probability.

Probability is the measure of how an event is likely to occur out of the number of possible outcomes. Calculating probabilities allows you to use logic and reason even with some degree of uncertainty. Find out how you can do the math when you calculate probabilities.

Answer: P(x < 2000) = ?

z = (2000 - 3000)/400 = -2.5

P(x < 2000) = P(z < -2.5)

= 0.0062 (Ans.) z(2000) = (2000-3000)/400 = -1000/400 = -5/2

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P(x < 2000) = P(z < -5/2) = binomcdf(-100,-5/2) = 0.0062

2) In what situation does one need probability theory? situations when certainty can be measured

Probability theory is applied to situations where uncertainty exists.

These situations include

1. The characterization of traffic at the intersection US 460 and Peppers Ferry Road (i.e., the number of cars that cross the intersection as a function of time)

2. The prediction of the weather in Blacksburg

3. The number of students traversing the Drill Field between 8:50 and 9:00 on Mondays

4. The thermally induced (Brownian) motion of molecules in a

(a) copper wire

(b) a JFET amplifier

3) Define the concept of sample space, sample points and events in context of probability theory.

Probability theory is concerned with real life situations where a person performs an experiment the outcome of which may not be certain. Such an experiment is called a random experiment. Games of change are classic examples of random experiments - the outcome of throwing a dice is not known with certainty prior to the throw. Firing a rocket is an example of performing a random experiment – it could result in failure or success. Associated with any random experiment is a set S of all possible outcomes – this set S