Question

In: Statistics and Probability

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 that will have a life between 304 and 596 hours.

Solutions

Expert Solution

orchestra answered 1 year ago
Next > < Previous

Related Solutions

A certain brand of light bulb is advertised to last 1600 hours. Suppose that the lifetimes...
A certain brand of light bulb is advertised to last 1600 hours. Suppose that the lifetimes of the light bulbs are normally distributed with a mean lifetime of 1650 hours and a standard deviation of 60 hours. (a) Sketch the normal distribution, go out 3 standard deviations. (b) What proportion of the light bulbs last at least the advertised time of 1600 hours? P(x ≥ 1600) = (Use the normalcdf on your graphing calculator.) (c) What proportion of light bulbs...
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
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...
A light bulb manufacturer guaran tees that the mean life of a certain type of light...
A light bulb manufacturer guaran tees that the mean life of a certain type of light bulb is at least 750 hours. A random sample of 250 light bulbs has a mean life of 745 hours. The population standard deviation standard deviation is 60 hours. Test the manufacturer's claim is at  . a) Write the null and alternative hypotheses and tell which is the claim. b) Write the P-value and how you calculated it. (what you typed into the calculator) c)...
Suppose the life time of a certain brand of light bulbs is exponentially distributed with an...
Suppose the life time of a certain brand of light bulbs is exponentially distributed with an average of 1000 hours. a. What’s the probability that a new light bulb won’t be able to reach this amount of time? b. What’s the probability that a new light bulb will have a life between 1000 and 2000 hours? c. Given that a light bulb has been working for 1000 hours, what’s the probability that it can work for another 2000 hours or...
A new extended-life light bulb has an average life of 750 hours, with a standard deviation...
A new extended-life light bulb has an average life of 750 hours, with a standard deviation of 50 hours. If the life of these light bulbs approximates a normal distribution, about what percent of the distribution will be between 650 hours and 850 hours?
The lifetime of a certain brand of electric light bulb is known to have a standard...
The lifetime of a certain brand of electric light bulb is known to have a standard deviation of 46 hours. Suppose that a random sample of 80 bulbs of this brand has a mean lifetime of 480 hours. Find a 90% confidence interval for the true mean lifetime of all light bulbs of this brand. Then complete the table below. Carry your intermediate computations to at least three decimal places. Round your answers to one decimal place. (If necessary, consult...
The lifetime of a certain brand of electric light bulb is known to have a standard...
The lifetime of a certain brand of electric light bulb is known to have a standard deviation of 51 hours. Suppose that a random sample of 70 bulbs of this brand has a mean lifetime of 493 hours. Find a 95% confidence interval for the true mean lifetime of all light bulbs of this brand. Then complete the table below. Carry your intermediate computations to at least three decimal places. Round your answers to one decimal place. (If necessary, consult...
Suppose that the life expectancy of a certain brand of nondefective light bulbs is normally​ distributed,...
Suppose that the life expectancy of a certain brand of nondefective light bulbs is normally​ distributed, with a mean life of 1100 hr and a standard deviation of 50 hr. If 70,000 of these bulbs are​ produced, how many can be expected to last at least 1100 hr? The number of light bulbs that can be expected to last at least 1100 hr is ______.
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT