Which type of bulb is most likely in the unmarked box

Assignment Help Basic Statistics

Reference no: EM131214845

A certain light bulb manufacturer makes two types of bulbs, a low-cost short-life (Stype) bulb and a more expensive long-life (L-type) bulb.

The two types of bulbs look identical and so the company must be sure to carefully label the boxes of bulbs. A box of bulbs is found on the floor of the manufacturing plant that (you guessed it) has not been labeled. In order to determine which types of bulbs are in the box, a promising young engineer suggested that they take one bulb from the box and run it until it burns out.

After observing how long the bulb remains lit, they should be able to make a good guess as to which type of bulbs are in the box. It is known that the length of time (in hours), X, that a bulb lasts can be described by a geometric random variable.

The parameter that appears in the above expression is for the S-type bulbs and for the L-type bulbs. It is known that of all the light bulbs the company manufactures 75% are S-type and 25% are L-type. Hence, before the experiment is run, the box in question has a 75% chance of being S-type and 25% chance of being L-type.

(a) If, after running the proposed experiment, it is observed that the bulb burned out after 200 hours, which type of bulb is most likely in the unmarked box? Mathematically justify your answer.

(b) What is the probability that your decision in part (a) turns out to be wrong? That is, if you decided that the box most likely contained L-type bulbs, what is the probability that the box actually contains S-type bulbs (or if you decided the box most likely contained S-type bulbs, what is the probability that the box actually contains L-type bulbs)?

Reference no: EM131214845

Questions Cloud

Non-current asset accounts : ALZ had the following balances on its non-current asset accounts at:31 March 2014 31 March 2013$000 $000Tangible assets:Property, plant and equipment 27,660 28,000Intangible assets:

How could you apply this law in your life on earth today : "A space explorer moving through the middle of intergalactic space, very far from any planet or star, notices a large rock floating around the cabin of the spaceship. The explorer wishes to take it as a specimen from an alien planet. Should he pus..

Describe problems you encounter in entering foreign market : Write a 1-2 page essay where in you choose a nation state in which you would like to open and operate a business. In your essay describe the problems you might encounter in entering the foreign market and in operating your business in that nation.

Heart at differentiating all other methods : What is meant by a case? When we do case studies, we have to figure out what is the case and what is X a case of? This concept is the heart at differentiating all other methods to a case study.

Which type of bulb is most likely in the unmarked box : If, after running the proposed experiment, it is observed that the bulb burned out after 200 hours, which type of bulb is most likely in the unmarked box?

How leadership style and actions affects the expectations : BUSM 1282: Project Management Leadership Assessment: Case study of project leadership. For you to better understand how leadership style and actions affects the expectations of and delivery of project success; to better understand the role of emoti..

How process hazards analysis can be used in the development : How do the labeling requirements of OSHA's Hazard Communication Standard contribute to risk reduction in the chemical process industries? Provide examples in your response.

Calculate first two resonant frequencies of the resonator : Suppose the short on the right-hand side is removed (Figure 14.27b). What are now the two lowest resonant frequencies?

Solve the monty hall problem : This classic problem was given widespread pop culture attention in 2008 by the movie "21."- Correct the given tricky problem.

User Account

All Pages