The points N(-3,-3)(−3,−3), O(-3,-9)(−3,−9), and P(5,-3)(5,−3) form a triangle. Plot the points then click the "Graph Triangle"
1 answer:
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Answer:
a) (26.50;57.50)
b) (117.34;128.66)
c) (12.13;27.87)
d) (-4.73;11.01)
e) No. Since the sample sizes are large (n ≥ 30), the central limit theorem guarantees that is approximately normal, so the confidence intervals are valid
Step-by-step explanation:
The central limit theorem states that "if we have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed. This will hold true regardless of whether the source population is normal or skewed, provided the sample size is sufficiently large".
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The confidence interval is given by this formula:
(1)
And for a 95% of confidence the significance is given by , and
. Since we know the population standard deviation we can calculate the critical value
Part a
If we use the formula (1) and we replace the values we got:
The 95% confidence interval is given by (26.50;57.50)
Part b
If we use the formula (1) and we replace the values we got:
The 95% confidence interval is given by (117.34;128.66)
Part c
If we use the formula (1) and we replace the values we got:
The 95% confidence interval is given by (12.13;27.87)
Part d
If we use the formula (1) and we replace the values we got:
The 95% confidence interval is given by (-4.73;11.01)
Part e
No. Since the sample sizes are large (n ≥ 30), the central limit theorem guarantees that is approximately normal, so the confidence intervals are valid
480700. The different combinations of students that could go on the trip with a total of 25 student, but only 18 may go, is 480700.
The key to solve this problem is using the combination formula . This mean the number of ways to choose a sample of r elements from a set of n distinct objects where order does not matter and replacements are not allowed.
The total of students is n and the only that 18 students may go is r: