A circle of radius 5 has its center in the first quadrant and is tangent to the x-axis at (1,0).
1 answer:
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Answer:
a) A sample of 256 was used in this survey.
b) 45.14% probability that the point estimate was within ±15 of the population mean
Step-by-step explanation:
This question is solved using the normal probability distribution and the central limit theorem.
Normal probability distribution
When the distribution is normal, we use 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 normally distributed random variable X, with mean and standard deviation
, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean
and standard deviation
.
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
a. How large was the sample used in this survey?
We have that . We want to find n, so:
A sample of 256 was used in this survey.
b. What is the probability that the point estimate was within ±15 of the population mean?
15 is the bounds with want, 25 is the standard error. So
Z = 15/25 = 0.6 has a pvalue of 0.7257
Z = -15/25 = -0.6 has a pvalue of 0.2743
0.7257 - 0.2743 = 0.4514
45.14% probability that the point estimate was within ±15 of the population mean
Answer:
B, C, and D.
Step-by-step explanation:
Let's go through each answer choice.
A: To find the slope of a line from two points, we use this formula: . Plugging in the values (-2,0) and (2, -4), we get:
Because option A says the slope is 1, but we got -1, option A is false.
B: To find the y-intercept, we use this formula:
Since we know the value of b is the y-intercept, we could write the y-intercept as (0,-2). Therefore, option B is true.
C: The equation of a line (in slope-intercept form) is y = mx + b, where y - y-coordinate, m = slope, x = x-coordinate, and b = y-intercept. Since we already solved for the y-intercept and slope, let's plug in those values:
As you can see, the equation we got here matches the one in option C, meaning it's true.
D: We know that a point is written like this: (x, y). If the x-coordinate is not zero but the y-coordinate is, then it's the x-intercept. Since the question says that (-2,0) is one of the points the line passes through, and option D says that the x-intercept is (-2,0), it's true.