Mathematics, 15.07.2019 11:30, hdjsjfjruejchhehd

Based upon a smaller sample of only 170 st. paulites, what is the probability that the sample proportion will be within of the population proportion (to 4 decimals). probability

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Given that in 2008 the Better Business Bureau settled 75% of complaints they received (USA Today, March 2, 2009). Suppose you have been hired by the Better Business Bureau to investigate the complaints they received this year involving new car dealers. You plan to select a sample of new car dealer complaints to estimate the proportion of complaints the Better Business Bureau is able to settle. Assume the population proportion of complaints settled for new car dealers is .75, the same as the overall proportion of complaints settled in 2008.

Part a) :

Suppose you select a sample of 450 complaints involving new car dealers. Show the sampling distribution of (to 4 decimals).

Population proportion = 0.75
sample size. n = 450
$Standard\ error=\sqrt{\frac{p(1-p)}{n}} \\ \\ =\sqrt{\frac{(0.75)(0.25)}{450}} = 0.0204$

Therefore, the sampling distribution has a proportion of 0.75 and a standard error of 0.0204.

Part b) :

Based upon a sample of 450 complaints, what is the probability that the sample proportion will be within .04 of the population proportion (to 4 decimals)?

The probability that the sample proportion will be within 0.04 of the population proportion is given by:

$P(p\ \textless \ 0.75\pm0.04)=2P\left(z\ \textless \ \frac{0.04}{0.0204} \right)-1 \\ \\ 2P(z\ \textless \ 1.961)-1=2(0.97505)-1=1.9501-1 \\ \\ =\bold{0.9501}$

Therefore, the probability that the sample proportion will be within .04 of the population proportion is 0.9501.

Part C:

Suppose you select a sample of 200 complaints involving new car dealers. Show the sampling distribution of (to 4 decimals).

Population proportion = 0.75
sample size. n = 200
$Standard\ error=\sqrt{\frac{p(1-p)}{n}} \\ \\ =\sqrt{\frac{(0.75)(0.25)}{200}} = 0.0306$

Therefore, the sampling distribution has a proportion of 0.75 and a standard error of 0.0306.

Part D):

Based upon the smaller sample of only 200 complaints, what is the probability that the sample proportion will be within .04 of the population proportion (to 4 decimals)?

The probability that the sample proportion will be within 0.04 of the population proportion is given by:

$P(p\
 \textless \ 0.75\pm0.04)=2P\left(z\ \textless \ \frac{0.04}{0.0306} 
\right)-1 \\ \\ 2P(z\ \textless \ 1.306)-1=2(0.90429)-1=1.80858-1 \\ \\
 =\bold{0.8086}$

Therefore, the probability that the sample proportion will be within .04 of the population proportion is 0.8086.

answered: Guest

answer: the answer is one of

$f=\dfrac{1}{2},~\dfrac{1}{4},~\dfrac{3}{4},~\dfrac{1}{6},~\dfrac{5}{6},~\dfrac{1}{8},~\dfrac{3}{8},~\dfrac{5}{8},~\dfrac{7}{8}.$

step-by-step explanation: we are given to write a proper fraction where the whole is divided into an even number of equal parts less than ten, and an odd number of those parts exist.

an even number less than 10 may be one of 2, 4, 6 or 8. so, the whole may be one of these four evens.

now, an odd number of these parts must exist, so the numerator must be an odd number, one of 1, 3, 5 or 7. it cannot be 9 because then the fraction will become improper.

thus, our fraction may be one of the following

$f=\dfrac{1}{2},~\dfrac{1}{4},~\dfrac{3}{4},~\dfrac{1}{6},~\dfrac{5}{6},~\dfrac{1}{8},~\dfrac{3}{8},~\dfrac{5}{8},~\dfrac{7}{8}.$

answered: Guest

3were boys and 5 were girls