Question

In: Math

A new LED light to replace incandescent bulbs has come on the market. The box says...

A new LED light to replace incandescent bulbs has come on the market. The box says it has an average life of 8000 hours with a standard deviation of 200 hours.

A.) What is the probability that a single bulb will last between 7950 and 8100 hours?

B.) What is the probability that the mean of a sample of 75 bulbs picked at random will be between 7950 and 8100 hours?

Solutions

Expert Solution

Solution :

(a)

P(7950 < x < 8100) = P[(7950 - 8000)/ 200) < (x - ) /  < (8100 - 8000) / 200) ]

= P(-0.25 < z < 0.5)

= P(z < 0.5) - P(z < -0.25)

= 0.2902

(b)

= / n = 200 / 75

= P[(7950 - 8000) / 200 / 75 < ( - ) / < (8100 - 8000) / 200 / 75)]

= P(2.165 < Z < 4.33)

= P(Z < 4.33) - P(Z < 2.165)

= 0.0152

milcah answered 2 months ago
Next > < Previous

Related Solutions

A new LED light to replace incandescent bulbs has come on the market. The box says...
A new LED light to replace incandescent bulbs has come on the market. The box says it has an average life of 9,000 hours with a standard deviation of 300 hours. a) What is the probability that a single bulb will last between 8950 and 9100 hours? b) What is the probability that the mean of a sample of 70 bulbs picked at random will be between 8950 and 9100 hours?
The city of Metropolis is considering replacing incandescent bulbs in traffic lights with light-emitting diode (LED)...
The city of Metropolis is considering replacing incandescent bulbs in traffic lights with light-emitting diode (LED) lights because they use significantly less energy and last much longer without abrupt failure. Currently Metropolis has 80,000 incandescent bulbs in traffic lights at approximately 12,000 intersections. It is estimated that replacing all the incandescent bulbs with LED will cost $46.02 million. However, the investment is also estimated to save the city $8.85 million per year in energy costs. Answer the following questions on...
Compact fluorescent bulbs are much more efficient at producing light than are ordinary incandescent bulbs. They...
Compact fluorescent bulbs are much more efficient at producing light than are ordinary incandescent bulbs. They initially cost much more, but last far longer and use much less electricity. According to one study of these bulbs, a compact bulb that produces as much light as a 100 W W incandescent bulb uses only 23.0 W W of power. The compact bulb lasts 10000 hours, on the average, and costs $ $ 11.00, whereas the incandescent bulb costs only $ $...
Compact fluorescent bulbs are much more efficient at producing light than are ordinary incandescent bulbs. They...
Compact fluorescent bulbs are much more efficient at producing light than are ordinary incandescent bulbs. They initially cost much more, but last far longer and use much less electricity. According to one study of these bulbs, a compact bulb that produces as much light as a 100 Wincandescent bulb uses only 23.0 W of power. The compact bulb lasts 1.00×104 hours, on the average, and costs $ 12.0 , whereas the incandescent bulb costs only 76.0 ¢, but lasts just...
The electric usage of LED is 8 watts and incandescent bulbs take up 40 watts. The...
The electric usage of LED is 8 watts and incandescent bulbs take up 40 watts. The lifetime of LED bulbs is 25 000 hours and the lifetime for incandescent bulb is 2500 hours. How much energy could be saved each year by replacing incandescent bulbs with LED bulbs? Assume that six 40-watt lamps arer lit an average of three hours a night and they are each replaces with 8 watt LED-bulbs.
A box contains six 25-watt light bulbs, nine 60-watt light bulbs, and five 100-watt light bulbs....
A box contains six 25-watt light bulbs, nine 60-watt light bulbs, and five 100-watt light bulbs. What is the probability a randomly selected a 60 watt light bulb? (PLease explain how did you get your answer)(2 pt) Note: You must provide your answer as a fraction NOT decimal) Cell Phone Provider Probability AT&T 0.271 Sprint 0.236 T–Mobile 0.111 Verizon 0.263 Does the above table represent the probability model? Explain your answer. (2 pt) The data shows the distance that employees...
In a box of 12 light bulbs, it is known that 5 of them are defective....
In a box of 12 light bulbs, it is known that 5 of them are defective. That is, 5 are defective and 7 function properly. We select 2 bulbs from the bag at random, without replacement. Find the probability they both function properly. Show work. Round your answer to 3 decimal places.
Is a ban on incandescent bulbs socially efficient? What about leaving the decision to the market?...
Is a ban on incandescent bulbs socially efficient? What about leaving the decision to the market? Explain your answer with a graph.
An incandescent lightbulb draws 590 mA, while an LED with the same light output draws 91.7...
An incandescent lightbulb draws 590 mA, while an LED with the same light output draws 91.7 mA. Both operate on standard 120-V household power. Part A Determine the energy-consumption rate of the incandescent lightbulb. Part B Part complete Determine the energy-consumption rate of the LED. Part C Suppose you've been operating the incandescent bulb for 3 hours a day and that your electrical energy costs 14.2 ¢/kWh¢/kWh. How much money will you save on your electric bills over a year...
Light emitting diode (LED) light bulbs have become required in recent years, but do they make...
Light emitting diode (LED) light bulbs have become required in recent years, but do they make financial sense? Suppose a typical 60-watt incandescent light bulb costs $.46 and lasts for 1,000 hours. A 15-watt LED, which provides the same light, costs $3.45 and lasts for 12,000 hours. A kilowatt-hour is 1,000 watts for 1 hour. Suppose you have a residence with a lot of incandescent bulbs that are used on average 500 hours a year. The average bulb will be...
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT