Answer:
The probability that the sample proportion will differ from the population proportion by greater than 0.03 is 0.009.
Step-by-step explanation:
According to the Central limit theorem, if from an unknown population large samples of sizes n > 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:

As the sample size is large, i.e. <em>n</em> = 492 > 30, the central limit theorem can be used to approximate the sampling distribution of sample proportion by the normal distribution.
The mean and standard deviation of the sampling distribution of sample proportion are:

Compute the probability that the sample proportion will differ from the population proportion by greater than 0.03 as follows:

![=P(|Z|>2.61)\\\\=1-P(|Z|\leq 2.61)\\\\=1-P(-2.61\leq Z\leq 2.61)\\\\=1-[P(Z\leq 2.61)-P(Z\leq -2.61)]\\\\=1-0.9955+0.0045\\\\=0.0090](https://tex.z-dn.net/?f=%3DP%28%7CZ%7C%3E2.61%29%5C%5C%5C%5C%3D1-P%28%7CZ%7C%5Cleq%202.61%29%5C%5C%5C%5C%3D1-P%28-2.61%5Cleq%20Z%5Cleq%202.61%29%5C%5C%5C%5C%3D1-%5BP%28Z%5Cleq%202.61%29-P%28Z%5Cleq%20-2.61%29%5D%5C%5C%5C%5C%3D1-0.9955%2B0.0045%5C%5C%5C%5C%3D0.0090)
Thus, the probability that the sample proportion will differ from the population proportion by greater than 0.03 is 0.009.
Hello!
An equivalent fraction is a fraction that is equal to another but is just written different. For example 1/2 and 3/6. They are both one half of the whole. 3/6 is just put into smaller pieces, but they equal the same thing.
I hope this helps!
Answer:
I = $ 1,937.50
Equation:
I = Prt
Calculation:
First, converting R percent to r a decimal
r = R/100 = 3.875%/100 = 0.03875 per year,
then, solving our equation
I = 10000 × 0.03875 × 5 = 1937.5
I = $ 1,937.50
The simple interest accumulated
on a principal of $ 10,000.00
at a rate of 3.875% per year
for 5 years is $ 1,937.50.
Step-by-step explanation:
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