Mathematics: Amanufacturer wishes to estimate the proportion of washing machines leaving the factory that is defective. how large a sample should she check in order to be 90% that the true proportion is within 1.5%?

Amanufacturer wishes to estimate the proportion of

mmoniquee

16.03.2022

Given:

ME = 1.5% = 0.015

P = 0.5 ( maximises P)

Answer and Step-by-step explanation:

Now,

Margin of Error (ME) is given by the formula:

$ME = t\times \ sigma$

where,

t = critical value = 1.645

$\sigma$ = standard deviation

So, squaring both sides and then rearranging:

$ME^{2} = t^{2}\times {\frac{P(1 - P)}{n}}$

$n = t^{2}\times {\frac{P(1 - P)}{ME^{2}}}$

n = (1.645)^{2}\times {\frac{0.5(1 - 0.5)}{0.015^{2}}}

n = 3006.69

n = 3007 (approx)

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