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tia_tia [17]
3 years ago
10

A polymer is manufactured in a batch chemical process. Viscosity measurements show that it is approximately normally distributed

with a standard deviation of 20. A random sample of 42 batches has a mean viscosity of 759. Construct a 99% confidence interval around the true population mean viscosity.
Mathematics
1 answer:
PilotLPTM [1.2K]3 years ago
3 0

Answer: (751.05, 766.95)

Step-by-step explanation:

We know that the confidence interval for population mean is given by :-

\overline{x}\pm z*\dfrac{\sigma}{\sqrt{n}},

where \sigma =population standard deviation.

\overline{x}= sample mean

n= sample size

z* = Two-tailed critical z-value.

Given :  \sigma= 20

n= 42

\overline{x}=759

We know that from z-table , the two-tailed critical value for 99% confidence interval : z* =2.576

Now, the 99% confidence interval around the true population mean viscosity :-

759\pm (2.5760)\dfrac{20}{\sqrt{42}}\\\\=759\pm (2.5760)(3.086067)\\\\=759\pm7.9497=(759-7.9497,\ 759+7.9497)\]\\=(751.0503,\ 766.9497)\approx(751.05,\ 766.95)

∴ A 99% confidence interval around the true population mean viscosity : (751.05, 766.95)

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