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podryga [215]
3 years ago
11

A random variable x x has a Normal distribution with an unknown mean and a standard deviation of 12. Suppose that we take a rand

om sample of size n = 36 n=36 and find a sample mean of ¯ x = 98 x¯=98 . What is a 95% confidence interval for the mean of x x ?
Mathematics
1 answer:
Paul [167]3 years ago
8 0

Answer:

95% Confidence Interval: (94.08,101.92)    

Step-by-step explanation:

We are given the following in the question:

Sample mean, \bar{x} = 98

Sample size, n = 36

Alpha, α = 0.05

Population standard deviation, σ = 12

95% Confidence Interval:

Formula:

\mu \pm z_{critical}\frac{\sigma}{\sqrt{n}}

Putting the values, we get,

z_{critical}\text{ at}~\alpha_{0.05} = 1.96

98 \pm 1.96(\dfrac{12}{\sqrt{36}} ) = 98 \pm 3.92 = (94.08,101.92)

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How many solutions does the following equation have? ln(x2 + 4x − 5) = 0
lisov135 [29]
Alrighty
remember
log_a(b)=c means a^c=b
and
ln(x)=log_e(x)
and
x^0=1 for all real values of x
so

ln(x^2+4x-5)=0 means
log_e(x^2+4x-5)=0 means
e^0=x^2+4x-5 which simplifies to
1=x²+4x-5
minus 1 both sides
0=x²+4x-6
use quadratic formula or complete the square
x=-2+\sqrt{10} and x=-2-\sqrt{10}
2 solutions
7 0
3 years ago
Which equation can be used to solve for x in the parallelogram below?
densk [106]

Answer:

B. (3x - 12)° = (2x + 8)°

Step-by-step explanation:

This equation can be used to solve x.

3x - 12 = 2x + 8

3x - 2x = 12 + 8

x = 20°

-------------------------------------------------------------------

Verification:

3(20) - 12 = 2(20) + 8

60 - 12 = 40 + 8

48° = 48°

6 0
3 years ago
What is the slope of the line determined by the equation -1/2x+3/4y=0
kvasek [131]

Answer:

The slope is 2/3

Step-by-step explanation:

-1/2x+3/4y=0

To find the slope, we need to get the equation in the form y= mx+b

Add 1/2x to each side

-1/2x+ 1/2 x+3/4y=0+1/2x

3/4 y = 1/2x

Multiply  by 4/3 to isolate y

4/3 * 3/4 y = 4/3 * 1/2 x

y = 2/3 x

The slope is 2/3 and the y intercept is 0

7 0
4 years ago
What do you add 15/4 to make 4
koban [17]
The answer would be 1/4 or \frac{1}{4} i hope this answer helps!
8 0
4 years ago
Which rule describes the function in the graph below?
m_a_m_a [10]

The function that models the graph is given as:f(x)=\left \{ {{-\frac{1}{3}x+\frac{4}{3}  \ \ -8 < x < 2} \atop {-x^2+6\ \ -2 < x < 0}} \atop {6\ \ 0 < x < 4}, \ \ x+2\ \  4 < x < 7 \right.

<h3>What is an equation?</h3>

An equation is an expression that shows the relationship between two or more numbers and variables.

The equation shown in the graph represents a piecewise function. Hence:

From the line through the point (-8, 4) and (-2, 2), the equation is f(x) = -(1/3)x + 4/3

From the curve through the point (-2, 2) and (0, 6), the equation is f(x) = -x² + 6

From the line through the point (0, 6) and (4, 6), the equation is f(x) = -6

From the line through the point (4, 6) and (7, 9), the equation is f(x) = x + 2

The function that models the graph is given as:f(x)=\left \{ {{-\frac{1}{3}x+\frac{4}{3}  \ \ -8 < x < 2} \atop {-x^2+6\ \ -2 < x < 0}} \atop {6\ \ 0 < x < 4}, \ \ x+2\ \  4 < x < 7 \right.

Find out more on equation at: brainly.com/question/2972832

#SPJ1

3 0
2 years ago
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