Assume that we want to construct a confidence interval. Do one of the following, as appropriate: (a) find the critical value t
1 answer:
Answer:
To construct a confidence interval, Normal distribution should be used since the sample size is quite large (n > 30)
From the z-table, at α = 0.025 the critical value is
Step-by-step explanation:
We are given the following information:
The sample size is
The mean weight is
The standard deviation is
Since the sample size is quite large (n > 30) then according to the central limit theorem the sampling distribution of the sample mean will be approximately normal, therefore, we can use the Normal distribution for this problem.
The correct option is (b)
The critical value corresponding to 95% confidence level is given by
Significance level = α = 1 - 0.95 = 0.05/2 = 0.025
From the z-table, at α = 0.025 the critical value is
What is Normal Distribution?
A Normal Distribution is a continuous probability distribution and is symmetrical around the mean. The shape of this distribution is like a bell curve and most of the data is clustered around the mean. The area under this bell shaped curve represents the probability.
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Solution
Asymptote:
Vertical Asymptote
- The vertical asymptotes of a rational function are determined by the denominator expression.
- The expression given is:
- The denominator of (x- 36) determines the asymptote line.
- The vertical asymptote defines where the rational function isundefined. Iin order for a rational function to be undefined, its denominator must be zero.
- Thus, we can say:
- Thus, the vertical asymptote is
Horizontal Asymptote:
- The horizontal asymptote exists in two cases:
1. When the highest degree of the numerator is less han the degree of the demnominator. In this case, the horizontal asymptote is y = 0
2. When the highest degee sof the numerator and tdenominator are the same. In this case, the horizontal asymptote is
- For our question, we can see that the highest degrees of the numerator and denominator are the same. Thus, we have the Horizontal Asymptote to be:
End behavior:
- The end behavior is examining the y-values of the function as x tendsto negative and positive infinity.
- Thus, we have that:
Final Answers
Asymptotes:
End behavior:
Answer: