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Shape of the Sampling Distribution of sample mean

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The print on the package of 100-watt General Electric soft-white light bulbs claims that these bulbs have an average life of 750 hours. Assume that the lives of all such bulbs have a normal distribution with a mean of 750 hours and a standard deviation of 55 hours. Let x (sample mean) be the mean life of a range sample of 25 such bulbs. Find the mean deviation of x (sample mean), and describe the shape of its sampling distribution.

Refer to above question. The print on the package of 100-watt General Electric soft white light-bulbs says that these bulbs have an average life of 750 hours. Assume that the lives of all such bulbs have a normal distribution with a mean of 750 hours and a standard deviation of 55 hours. Find the probability that the mean life of a random sample of 25 such bulbs will be
a. greater than 735 hours
b. between 725 and 740 hours
c. within 15 hours of the population mean
d. less than the population mean by 20 hours or more

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Solution Summary

Step by step method for computing probability based on normal distribution.

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Sampling Distribution and Population Distribution

I assume my scenario will have to include enough information to answer the questions below so I will need help with this one as well

Create and write your own scenario about a specific population. Then, answer the following questions about your scenario:

What are the mean, standard deviation, and shape of the population distribution?

What are the mean, standard deviation and shape of the sample?

What are the mean, standard error and shape of the sampling distribution of the sample mean?

Is it possible for the shapes of these three distributions to be different? Describe a brief scenario where this may happen.

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