# A researcher believes that 7% of female smoke cigarets if the researchers correct what is probability that the proportion of smokers in a sample of 445 females were different from population proportion by greater than 3% ? Round to 4 decimal places

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A researcher believes that 7% of female smoke cigarets if the researchers correct what is probability that the proportion of smokers in a sample of 445 females were different from population proportion by greater than 3% ? Round to 4 decimal places

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Step 1

Calculation:

Denote π as the true population proportion of female smokers. Hence, π = 0.07.

Denote p as the sample proportion in a sample of n = 445 females.

The sample size is very large. Moreover, = 445 ∙ (0.07) = 31.15 > 5; n (1 – π) = 445 ∙ (1 – 0.07) = 413.85 > 5.

Hence, according to the Central Limit Theorem for proportion, p follows the normal distribution, with parameters- mean µ ...

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