##### Question

In: Statistics and Probability

# A lab tested the ibuprofen content in a drug manufacturer’s headache pills. After testing 500 random...

A lab tested the ibuprofen content in a drug manufacturer’s headache pills. After testing 500 random samples, the mean ibuprofen content was found to be 202 mg with a standard deviation of 10 mg. Construct a 99% confidence interval for the true mean ibuprofen content in all of the manufacturer’s headache pills.

## Solutions

##### Expert Solution

Solution :

Given that,

Point estimate = sample mean = = 202

Population standard deviation =    =  10
Sample size = n =

At 99% confidence level the z is ,

= 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

Z/2 = Z0.005 = 2.576   ( Using z table )

Margin of error = E = Z/2* ( /$\sqrt$n)

= 2.576* ( 10 / $\sqrt$ 500)

= 1.1520

At 99% confidence interval estimate of the population mean is,

- E < < + E

202-1.1520 < < 202+1.1520

200.8480< < 203.1520

(200.8480,203.1520)

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