Question

A large urgent care Center found that they can see an average of 28 patients per hour assume the standard deviation is 3.3 a random sample of 40 patients were selected find the 95% confidence interval of the mean

Answer 1

Answer

The 95% confidence interval of the mean is {26.9766, 28.0234}

Explanation

Given data:

Sample mean, x = 28 patients

Standard deviation, s = 3.3

Sample size = 40 patients

z-value for 95% confidence interval = 1.96

The Confidence interval, CI, of the mean the formula is give by:

$CI=x\pm z\frac{s}{\sqrt[]{n}}$

Substitute the given parameters into the formula to get CI:

$\begin{gathered} CI=28\pm1.96\times\frac{3.3}{\sqrt[]{40}} \\ CI=28\pm1.96\times\frac{3.3}{6.32} \\ CI=28\pm1.96\times0.522151898 \\ CI=28\pm1.0234 \\ CI=\mleft\lbrace28-1.0234,28+1.0234\mright\rbrace \\ CI=\mleft\lbrace26.9766,28.0234\mright\rbrace \end{gathered}$