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Naya [18.7K]
3 years ago
8

a random sample of 510 high school students has a normal distribution. The sample mean average ACT exam score was 21 with a 3.2

standard deviation. Construct a 99% confidence interval estimate of the population mean average ACT exam. Find the critical value​
Mathematics
1 answer:
34kurt3 years ago
8 0

Answer:

CI = 21 ± 0.365

Step-by-step explanation:

The confidence interval is:

CI = x ± SE * CV

where x is the sample mean, SE is the standard error, and CV is the critical value (either t score or z score).

Here, x = 21.

The standard error for a sample mean is:

SE = σ / √n

SE = 3.2 / √510

SE = 0.142

The critical value is looked up in a table or found with a calculator.  But first, we must find the alpha level and the critical probability.

α = 1 - 0.99 = 0.01

p* = 1 - (α/2) = 1 - (0.01/2) = 0.995

Using a calculator or a z-score table:

P(x<z) = 0.995

z = 2.576

Therefore:

CI = 21 ± 0.142 × 2.576

CI = 21 ± 0.365

Round as needed.

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The diagram rerpesents responses to a survey that include statements p and q . Which statement is true?
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Answer:

C. The number of responces p\vee q is also 46

Step-by-step explanation:

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From the diagram,

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Which values for A and B will create infinitely many solutions for this system of equations? ax-y=8 2x+y=b
Nata [24]

Answer:

a = -2 , b = -8

Step-by-step explanation:

* Lets talk about the solution of the linear equations

- There are three types of the solutions of the system of linear equations

# If the two lines intersect each other, then there is one solution

- The equations are ax+ by = c , dx + ey = f

# If the two lines parallel to each other, then there is no solution

- The equations are ax+ by = c , ax + by = d in its simplest form ,

  where a is the coefficient of x , b is the coefficient of y and

  c , d are the numerical terms

# If the two lines coincide (over each other), then there are infinite

   solutions

- The equations are ax+ by = c , ax + by = c in its simplest form, where

  a is the coefficient of x , b is the coefficient of y and c is the

  numerical term

* Lets solve the problem

∵ The system of equation is:

   ax - y = 8 ⇒ (1)

   2x + y = b ⇒ (2)

∵ The system create infinitely many solutions

∴ The lines are coincide

- The equations must be equal, then multiply equation(1) or (2) by -1 to

  make the coefficient of y in the two equations equal

∴ -ax + y = -8

∴ 2x + y = b

∵ Their coefficients of x are equal

∵ Their coefficients of y are equal

∵ Their numerical terms are equal

∵ The coefficient of x in equation (1) is -a and in equation (2) is 2

∴ -a = 2 ⇒ multiply both sides by -1

∴ a = 2

∵ The numerical term in equation (1) is -8 and in equation (2) is b

∴ b = -8

* The values for a and b will create infinitely many solutions are -2 , -8

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3 years ago
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