# Answer on Statistics and Probability Question for Jasmine

Question #18121

A random sample of 84 light bulbs had a mean life of 423 hrs with a standard deviation of 27hrs. Construct a 90% confidence interval for the mean life of all light bulbs of this type.

Expert's answer

we suppose that sample is ruled by student's distribution

so, step 1 is to check value of student's coefficient for alpha=1-0.9=0.1 and

degree of freedom = 423-1 = 422.

In tables you will find that it is approximately = 1.65

Next you have to divide your standard deviation by the square root of your

sample size.

that is 27/sqrt(423) = 1.31

now multiply them

1.33*1.65 = 4.851

So your 90% confidence interval is

so, step 1 is to check value of student's coefficient for alpha=1-0.9=0.1 and

degree of freedom = 423-1 = 422.

In tables you will find that it is approximately = 1.65

Next you have to divide your standard deviation by the square root of your

sample size.

that is 27/sqrt(423) = 1.31

now multiply them

1.33*1.65 = 4.851

So your 90% confidence interval is

**84+-4.851/2 = 84+- 2.4**Need a fast expert's response?

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