Question

In: Statistics and Probability

Suppose the life span of a light bulb is normally distributed with mean 1000 hours and...

Suppose the life span of a light bulb is normally distributed with mean 1000 hours and standard deviation 75 hours. (a) Find the 57th percentile of this distribution. (b) Find the probability that a random light bulb will last longer than 1100 hours. (c) Find the probability that the life span of a light bulb will be more than 3.14 standard deviations away from the mean. (d) Suppose you take a sample of 15 light bulbs and measure the average life span. Carefully justify whether the Central Limit Theorem applies, and if it does, find the probability that the average life span is between 950 and 1025 hours.

Solutions

Expert Solution

orchestra answered 1 year ago
Next > < Previous

Related Solutions

The life in hours of a 75-watt light bulb is known to be approximately normally distributed,...
The life in hours of a 75-watt light bulb is known to be approximately normally distributed, with standard deviation σ = 25 hours. A random sample of 62 bulbs has a mean life of x-bar = 1,014 hours. Construct a 98% confidence interval around the true population mean life of the light bulb.
2. The lifetime of light bulb is normally distributed with mean of 1400 hours and standard...
2. The lifetime of light bulb is normally distributed with mean of 1400 hours and standard deviation of 200 hours. a. What is the probability that a randomly chosen light bulb will last for more than 1800 hours? b. What percentage of bulbs last between 1350 and 1550 hours? c. What percentage of bulbs last less than 1.5 standard deviations below the mean lifetime or longer than 1.5 standard deviations above the mean? d. Find a value k such that...
The lifetime of light bulb is normally distributed with mean of 1400 hours and standard deviation of 200 hours.
The lifetime of light bulb is normally distributed with mean of 1400 hours and standard deviation of 200 hours. a. What is the probability that a randomly chosen light bulb will last for more than 1800 hours? b. What percentage of bulbs last between 1350 and 1550 hours? c. What percentage of bulbs last less than 1.5 standard deviations below the mean lifetime or longer than 1.5 standard deviations above the mean? d. Find a value k such that 20% of the bulbs last...
Suppose that a certain brand of light bulb has a mean life of 450 hours and...
Suppose that a certain brand of light bulb has a mean life of 450 hours and a standard deviation of 73 hours. Assuming the data are bell-shaped: (Show work to get full credit) a. Would it be unusual for a light bulb to have a life span of 320 hours? 615 hours? Justify each response. b. According to the Empirical Rule, 99.7% of the light bulbs have a lifetime between what two values? c. Determine the percentage of light bulbs...
A manufacturer of light bulbs finds that one light bulb model has a mean life span...
A manufacturer of light bulbs finds that one light bulb model has a mean life span of 1025 h with a standard deviation of 80 h. What percent of these light bulbs will last as follows? (Round your answers to one decimal place.) (a) at least 970 h % (b) between 810 and 880 h %
a company manufactures light bulb. the company want the bulbs to have a mean life span...
a company manufactures light bulb. the company want the bulbs to have a mean life span of 99t hours. this average is maintained by periodically testing random sample of 25 light bulbs. if the t-value fail between -t0.90 and t0.90, then the company will be satisfied that it is manufacturing acceptable light bulbs. for a random sample, the mean life span of the sample is 1000 hours and the standard deviation is 25 hours. assume the life span are approximately...
The life of a ventilator is normally distributed with a mean of 9000 hours and a...
The life of a ventilator is normally distributed with a mean of 9000 hours and a standard deviation of 500 hours. (a) What is the probability that the ventilator fails before 8000 hours? (b) What is the life in hours that is exceeded by 96% of the ventilators? (c ) If 20 such ventilators are used in a hospital, and they are assumed to fail independently, what is the probability that all 20 are still operating after 7500 hours?
The lifetimes of light bulbs are normally distributed with a mean of 500 hours and a...
The lifetimes of light bulbs are normally distributed with a mean of 500 hours and a standard deviation of 25 hours. Find the probability that a randomly selected light bulb has a lifetime that is greater than 532 hours. SHOW FULL WORK!
A light bulb manufacturer guarantees that the mean life of a certain type of light bulb...
A light bulb manufacturer guarantees that the mean life of a certain type of light bulb is at least 720 hours. A random sample of 51 light bulbs as a mean of 701.6 hours with a population standard deviation of 62 hours. At an α=0.05, can you support the company’s claim using the test statistic? claim is the alternative, reject the null and support claim as test statistic (-2.12) is not in the rejection region defined by the critical value...
A light bulb manufacturer guarantees that the mean life of a certain type of light bulb...
A light bulb manufacturer guarantees that the mean life of a certain type of light bulb is at least 757 hours. A random sample of 22 light bulbs has a mean life of 729 hours. Assume the population is normally distributed and the population standard deviation is 65 hours. At a=0.02​, do you have enough evidence to reject the​ manufacturer's claim. 1. identify null and alternative hypothesis 2.identify region rejections on graph 3.identify standarized test statstics 4. interpret decision
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT