Question

16#8

a)A poll of 80 students found that 38% were in favor of raising tution to build a new math building. The standard deviation of this poll is 6%. What would be the standard deviation if the sample size were increased from 80 to 162?

b) Fluorescent lightbulbs have lifetimes that follow a normal distribution, with an average life of 1,284 days and a standard deviation of 1,456 hours. In the production process the manufacturer draws random samples of 336 lightbulbs and determines the mean lifetime of the sample. What is the standard deviation, in hours, of this sample mean?

Answer #1

A) Note that the standard deviation of the sample proportion is inversely proportional to the square root of the sample size here. Therefore the new standard deviation here is computed as:

**Therefore 4.2164% is the required standard deviation
here.**

b) We are given the distribution here as:

The standard deviation of sample mean using the Central limit theorem here is given as:

**Therefore 79.4313 is the required value
here.**

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