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Advocard [28]
3 years ago
13

A sample of 64 was taken from a population, with the mean of the sample being 119 and the standard deviation of the sample being

16. What is the 95% confidence interval for the mean of the population?
A. (115, 123)
B. (117, 121)
C. (113, 125)
D. (118, 120)
Mathematics
1 answer:
Fofino [41]3 years ago
6 0
We have the sample size, sample mean and the sample standard deviation. Since the population standard deviation is not know, we will use t-distribution to find the confidence interval.

The critical t value for 95% confidence interval and 63 degrees of freedom is 1.998.

The 95% confidence for the population mean will be:

(119-1.998 *\frac{16}{ \sqrt{64} } ,119+1.998 *\frac{16}{ \sqrt{64} }) \\  \\ 
=(115.004, 122.996) \\ \\=(115,123)

Thus, the 95% confidence interval for the population mean will be (115,123)

So, option A is the correct answer
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Effectus [21]

By Euler's method the <em>numerical approximate</em> solution of the <em>definite</em> integral is 4.189 648.

<h3>How to estimate a definite integral by numerical methods</h3>

In this problem we must make use of Euler's method to estimate the upper bound of a <em>definite</em> integral. Euler's method is a <em>multi-step</em> method, related to Runge-Kutta methods, used to estimate <em>integral</em> values numerically. By integral theorems of calculus we know that definite integrals are defined as follows:

∫ f(x) dx = F(b) - F(a)     (1)

The steps of Euler's method are summarized below:

  1. Define the function seen in the statement by the label f(x₀, y₀).
  2. Determine the different variables by the following formulas:

    xₙ₊₁ = xₙ + (n + 1) · Δx     (2)
    yₙ₊₁ = yₙ + Δx · f(xₙ, yₙ)     (3)
  3. Find the integral.

The table for x, f(xₙ, yₙ) and y is shown in the image attached below. By direct subtraction we find that the <em>numerical</em> approximation of the <em>definite</em> integral is:

y(4) ≈ 4.189 648 - 0

y(4) ≈ 4.189 648

By Euler's method the <em>numerical approximate</em> solution of the <em>definite</em> integral is 4.189 648.

To learn more on Euler's method: brainly.com/question/16807646

#SPJ1

7 0
2 years ago
Which one was it? I’ve been trying for a while
Reika [66]
The answer is b (I think not really sure)
6 0
3 years ago
Read 2 more answers
"the sum of d and 9.
ozzi

Answer:

d+9

Step-by-step explanation:

sum implies addition

so you would add d and 9

since d is a variable the most you can simplify is

d+9

6 0
3 years ago
Read 2 more answers
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