A bulletin board has a perimeter of 200 inches. Which expression expresses the area A(w) of the bulletin board as a function of
1 answer:
Answer:
area A(w) of the bulletin board as a function of its width, w =[100-w]*w= 100w-
Step-by-step explanation:
- let, the shape of the bulletin board is a rectangle,
- then the perimeter of it = sum of all sides
= 2[length+width] = 2[l+w]
(let l: length, w : width )
- so, 200 = 2[l+w]
100= l+w ( dividing both the sides by 2)
so, l= 100-w
- area = length*width=l*w=[100-w]*w
- therefore,area A(w) of the bulletin board as a function of its width, w =[100-w]*w= 100w-
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Answer:
Probability that the sample proportion will be greater than 0.5 is 0.8133.
Step-by-step explanation:
We are given that the a particular candidate for public office is in fact favored by p = 48% of all registered voters. A polling organization is about to take a simple random sample of voters and will use the sample proportion to estimate p.
Suppose that the polling organization takes a simple random sample of 500 voters.
<em>Let </em><em> = sample proportion</em>
The z-score probability distribution for sample proportion is given by;
Z = ~ N(0,1)
where, = sample proportion
p = population proportion = 48%
n = sample of voters = 500
The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X.
So, probability that the sample proportion will be greater than 0.5 is given by = P( > 0.50)
P( > 0.50) = P(
<
) = P(Z < 0.89) = 0.8133
<em>Now, in the z table the P(Z </em><em> x) or P(Z < x) is given. So, the above probability is calculated by looking at the value of x = 0.89 in the z table which has an area of 0.8133.</em>
Therefore, probability that the sample proportion will be greater than 0.50 is 0.8133.