Question

The proportion of passengers who miss a flight for which they have a reservation is0.0995. Suppose a flight 290 reservations. Find the standard deviation of the sampleproportion, ºf, rounded to the nearest ten-thousandth (4 decimal places).

Answer 1

Answer

Standard deviation of the sample proportion = 0.0176

Explanation

For a distribution with proportion, p, the standard deviation of the sample proportion is given as

$\sigma_x=\sqrt[]{\frac{p(1-p)}{n}}$

where

p = sample proportion = 0.0995

n = sample size = 290

$\begin{gathered} \sigma_x=\sqrt[]{\frac{p(1-p)}{n}} \\ \sigma_x=\sqrt[]{\frac{0.0995(1-0.0995)}{290}} \\ \sigma_x=\sqrt[]{\frac{0.0995(0.9005)}{290}} \\ \sigma_x=\sqrt[]{\frac{0.08959975}{290}} \\ \sigma_x=\sqrt[]{0.0003089647} \\ \sigma_x=0.0176 \end{gathered}$

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