Question

In: Statistics and Probability

8.8. A manufacturing company of light bulb claims that an average light bulb lasts 500 days....

8.8. A manufacturing company of light bulb claims that an average light bulb lasts 500 days. A contractor randomly selects 30 bulbs for testing. The sampled bulbs last an average of 490 days, with a standard deviation of 100 days. If the claim were true, what is the probability that 30 randomly selected bulbs would have an average life of no more than 490 days? [10]

Solutions

Expert Solution

Here we use the concept of Normal Distribution , calculate the Z score, then calculate the probability


Related Solutions

A pharmaceutical company claims that the average cold lasts an average of 8.4 days. They are...
A pharmaceutical company claims that the average cold lasts an average of 8.4 days. They are using this as a basis to test new medicines designed to shorten the length of colds. A random sample of 106 people with colds, finds that on average their colds last 8.28 days. The population is normally distributed with a standard deviation of 0.9 days. At α=0.02, what type of test is this and can you support the company’s claim using the p-value? Claim...
A washing machine manufacturing company claims that an average washing machine lasts 300 days. A researcher...
A washing machine manufacturing company claims that an average washing machine lasts 300 days. A researcher randomly selects 15 machines for testing. The sample machines last an average of 290 days with a standard deviation of 50 days. If the company's claim is true, find the range of probability (area in right tail from the table) that 15 randomly selected machines would have an average life of no more than 290 days, in other words where does your t-statistic lie...
A company that manufactures light bulbs claims that its light bulbs last an average of 1500...
A company that manufactures light bulbs claims that its light bulbs last an average of 1500 hours. A consumer research group wants to test the hypothesis that the mean life of light bulbs manufactured by this company is less than 1500 hours. A sample of 35 light bulbs manufactured by this company gave a mean life of 1450 hours with a standard deviation of 100 hours. The significance level of the hypothesis test is 5% and the distribution for the...
A light-bulb manufacturer advertises that the average life for its light bulbs is 900 hours. A...
A light-bulb manufacturer advertises that the average life for its light bulbs is 900 hours. A random sample of 15 of its light bulbs resulted in the following lives in hours.                          995 590 510 539 739 917 571 555                          916   728   664   693   708   887   849 At the 10% significance level, test the claim that the sample is from a population with a mean life of 900 hours. Use the P-value method of testing hypotheses. Identify the null and alternative hypotheses,...
A company manufacturing light bulbs is testing a new model. The company claims that the mean...
A company manufacturing light bulbs is testing a new model. The company claims that the mean life time is less than 1000 hours. A sample of 16 light bulbs are found to have sample mean of 987.5 hours and a sample variance of 400. (a) Test this claim at the significance level α = 0.02. Step 1: Step 2: Step 3: Step 4: Step 5: (b) Is there any assumption needed to solve this question? if yes please state the...
A company that produces cell phones claims its standard phone battery lasts longer on average than...
A company that produces cell phones claims its standard phone battery lasts longer on average than other batteries in the market. To support this claim, the company publishes an ad reporting the results of a recent experiment showing that under normal usage,their batteries last at least 35 hours. To investigate this claim, a consumer advocacy group asked the company for the raw data. The company sends the group the following results: 35, 34, 32, 31, 34, 34, 32, 33, 35,...
(b)     A light bulb manufacturer requires no more than 10% defective light bulbs if the manufacturing...
(b)     A light bulb manufacturer requires no more than 10% defective light bulbs if the manufacturing process is to be considered working. Assuming the manufacturing process is producing only 10% defectives, what is the probability that a sample of 20 randomly selected light bulbs will contain exactly 2 defective light bulbs? Suppose the reliability of the manufacturing process is unknown. In a random sample of 10 light bulbs 5 defectives are found. Based on this result, the manufacturer wants to...
The average lifetime of a light bulb is 3000 hours with a standard deviation of 696...
The average lifetime of a light bulb is 3000 hours with a standard deviation of 696 hours. A simple random sample of 36 bulbs is taken. What is the probability that the average life in the sample will be greater than 3219.24? Note: respond in decimal form, for example, if your solution is 87.1234%, you should enter in 0.871234.
The average lifetime of a light bulb is 2850 hours with a standard deviation of 400....
The average lifetime of a light bulb is 2850 hours with a standard deviation of 400. A simple random sample of 30 bulbs is taken. What is the probability that the average life in the sample will be between 2600 and 2700 hours?
For an auto insurance company, the average cost of collision claims is $500 per year for...
For an auto insurance company, the average cost of collision claims is $500 per year for careful drivers and $3000 per year for poor drivers. The drivers are risk neutral and know whether they are careful or poor, but the insurance company only knows that 15% of drivers are poor. What is the insurance company's breakeven price for the collision insurance? A. $425 per year B. $450 per year C. $875 per year D. $2,625 per year
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT