Please answer the question in the photo
2 answers:
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What it means is, check the picture below.
so, the first part shows two rectangles... the rectangle goes from 1.0 to 1.6, so it has a width of 0.6.
and the height comes from the middle point, or 1.3 is f(1.3) = (1.3)² or 1.69.
so you get the area of the first rectangle, 0.6 * 1.69
and then you do the same for the second rectangle, it goes from 1.6 to 2.0, so is of width 0.4, and its height comes from the middle 1.8 point, is f(1.8) = (1.8)², or 3.24.
so its area is 0.6 * 3.24
then you add the areas of the rectangles to approximate the area under the parabola.
so, you'd do the same for the other part of the picture with the four rectangles.
the first rectangle of the four for example, has a width of 0.2 and a height of f(1.1) = (1.1)² or 1.21.
so, the first part shows two rectangles... the rectangle goes from 1.0 to 1.6, so it has a width of 0.6.
and the height comes from the middle point, or 1.3 is f(1.3) = (1.3)² or 1.69.
so you get the area of the first rectangle, 0.6 * 1.69
and then you do the same for the second rectangle, it goes from 1.6 to 2.0, so is of width 0.4, and its height comes from the middle 1.8 point, is f(1.8) = (1.8)², or 3.24.
so its area is 0.6 * 3.24
then you add the areas of the rectangles to approximate the area under the parabola.
so, you'd do the same for the other part of the picture with the four rectangles.
the first rectangle of the four for example, has a width of 0.2 and a height of f(1.1) = (1.1)² or 1.21.
Answer:
The correct 95% confidence interval is (8.4, 8.8).
Step-by-step explanation:
The information provided is:
(a)
The (1 - <em>α</em>)% confidence interval for population mean (<em>μ</em>) is:
The 95% confidence interval for the average satisfaction score is computed as:
8.6 ± 1.96 (2.2)
This confidence interval is incorrect.
Because the critical value is multiplied directly by the standard deviation.
The correct interval is:
(b)
The (1 - <em>α</em>)% confidence interval for the parameter implies that there is (1 - <em>α</em>)% confidence or certainty that the true parameter value is contained in the interval.
The 95% confidence interval for the mean rating, (8.4, 8.8) implies that the true there is a 95% confidence that the true parameter value is contained in this interval.
The mistake is that the student concluded that the sample mean is contained in between the interval. This is incorrect because the population is predicted to be contained in the interval.
(c)
The (1 - <em>α</em>)% confidence interval for population parameter implies that there is a (1 - <em>α</em>) probability that the true value of the parameter is included in the interval.
The 95% confidence interval for the mean rating, (8.4, 8.8) implies that the true mean satisfaction score is contained between 8.4 and 8.8 with probability 0.95 or 95%.
Thus, the students is not making any misinterpretation.
(d)
According to the Central Limit Theorem if we have a population with mean <em>μ</em> and standard deviation <em>σ</em> and we take appropriately huge random samples (<em>n</em> ≥ 30) from the population with replacement, then the distribution of the sample mean will be approximately normally distributed.
In this case the sample size is,
<em>n </em>= 500 > 30
Thus, a Normal distribution can be applied to approximate the distribution of the alumni ratings.
Answer: The maximum number of people who could answer yes for both cat and dog is 7.
Step-by-step explanation: Given that a survey of 100 people asked if they have a dog or a cat.
Out of those 100 people, 56 people answered yes for dog and 51 people answered yes for cat. Some people may own neither and some people may own both animals.
We are to find the maximum number of people that could answer yes for both cat and dog.
Let A and B represents the set of people that answered Yes for dog and Yes for cat respectively.
Then, according to the given information, we have
From Set Theory, we have
Since the total number of people is 100, so we get
Therefore, from equation (i), we get
Thus, the maximum number of people who could answer yes for both cat and dog is 7.