Question

A milk processor monitors the number of bacteria per millilitre in raw milk received at the factory. A random sample of 10 one-millilitre specimens of milk supplied by one producer gives the following data:

5370 4890 5100 4500 5260 5150 4900 4760 4700 4870

Construct and interpret a 90% confidence interval for the population mean $\mu$.

Short answer

The confidence interval for the population mean$\mu$is$(4794.4,5105.6)$

Step-by-step solution

introduction

A milk processor monitors the number of bacteria per millilitre in raw milk received at the factory.

Given data -

$5370489051004500526051504900476047004870$

explanation

Calculating the confidence interval CI,

n = $10$

$\stackrel{-}{x}=4950$and s =$268.45$

role="math" localid="1651643707213" $$\begin{gathered} \Rightarrow \overline{x}\pm z\frac{s}{\sqrt{n}} \\ =4950\pm 2.021\frac{268.45}{\sqrt{10}} \\ =(4794.4,5105.6) \end{gathered}$$

the confidence interval is$(4794.4,5105.6)$