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Answer:
The probability that the value of P will be less than 0.81 is 0.7642.
Step-by-step explanation:
According to the Central limit theorem, if from an unknown population large samples of sizes <em>n</em> > 30, are selected and the sample proportion for each sample is computed then the sampling distribution of sample proportion follows a Normal distribution.
The mean of this sampling distribution of sample proportion is:
The standard deviation of this sampling distribution of sample proportion is:
Given:
<em>n</em> = 100
<em>p</em> = 0.78
Since <em>n</em> = 100 > 30, according to the central limit theorem the sampling distribution of sample proportion follows a Normal distribution.
Compute the value of as follows:
*Use a <em>z</em>-table for the probability.
Thus, the probability that the value of P will be less than 0.81 is 0.7642.