Answer:
(-1, 6)
Step-by-step explanation:
A graphing calculator shows the vertex to be (x, y) = (-1, 6).
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You can also find it by putting the equation into vertex form.
y = -2(x^2 +2x) +4
y = -2(x^2 +2x +1) +4 +2(1) . . . . . add 1 inside parens; the opposite outside
y = -2(x +1)^2 +6
Compare to ...
y = a(x -h)^2 +k
and you see a=-2, h=-1, k=6
The vertex is (h, k) = (-1, 6).
Answer:
The probability that the mean amount of credit card debt in a sample of 1600 such households will be within $300 of the population mean is roughly 0.907 = 90.7%.
Step-by-step explanation:
To solve this question, we have to understand the normal probability distribution and the central limit theorem.
Normal probability distribution:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean and standard deviation
, the zscore of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value 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. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central limit theorem:
The Central Limit Theorem estabilishes that, for a random variable X, with mean and standard deviation
, a large sample size can be approximated to a normal distribution with mean
and standard deviation
In this problem, we have that:
The probability that the mean amount of credit card debt in a sample of 1600 such households will be within $300 of the population mean is roughly
This probability is the pvalue of Z when X = 1600 + 300 = 1900 subtracted by the pvalue of Z when X = 1600 - 300 = 1300. So
X = 1900
By the Central Limit Theorem
has a pvalue of 0.9535.
X = 1300
has a pvalue of 0.0465.
0.9535 - 0.0465 = 0.907.
The probability that the mean amount of credit card debt in a sample of 1600 such households will be within $300 of the population mean is roughly 0.907 = 90.7%.