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Jobisdone [24]
3 years ago
14

Consider the next 1000 90% CIs for μ that a statistical consultant will obtain for various clients. Suppose the data sets on whi

ch the intervals are based are selected independently of one another. How many of these 1000 intervals do you expect to capture the corresponding value of μ?
Mathematics
1 answer:
Ivenika [448]3 years ago
6 0

Answer:

90% CI expects to capture u 90% of time

(a) This means 0.9 * 1000 = 900 intervals will capture u

(b) Here we treat CI as binomial random variable, having probability 0.9 for success

n = 1000

p = 0.9

For this case, applying normal approximation to binomial, we get:

mean = n*p= 900

variance = n*p*(1-p) = 90

std dev = 9.4868

We want to Find : P(890 <= X <= 910) = P( 889.5 < X < 910.5) (integer continuity correction)

We convert to standard normal form, Z ~ N(0,1) by z1 = (x1 - u )/s

so z1 = (889.5 - 900 )/9.4868 = -1.11

so z2 = (910.5 - 900 )/9.4868 = 1.11

P( 889.5 < X < 910.5) = P(z1 < Z < z2) = P( Z < 1.11) - P(Z < -1.11)

= 0.8665 - 0.1335

= 0.733

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wheres the picture?

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3 years ago
10) Gabe put up a fence around his rectangular vegetable garden this weekend.
dybincka [34]

Answer:

The length is 16 ft, and the width is 3 ft.

Step-by-step explanation:

Let L = length & let W = width.

The perimeter of a rectangle is

P = 2(L + W)

The area of a rectangle is

A = LW

We know the perimeter and the area, so we substitute those values int he equations above and we switch sides in both equations.

Perimeter: 2(L + W) = 38

Divide both sides by 2:

L + W = 19

Area: LW = 48

We have a system of two equations in two unknowns:

L + W = 19

LW = 48

Solve the first equation for L and substitute it into the second equation.

L = 19 - W

(19 - W)W = 48

19W - W^2 - 48 = 0

Multiply both sides by -1, and rearrange the order of the terms.

W^2 - 19W + 48 = 0

(W - 16)(W - 3) = 0

W - 16 = 0 or W - 3 = 0

W = 16 or W = 3

Use W = 3 to find L

L = 19 - W

L = 19 - 3

L = 16

Answer: The length is 16 ft, and the width is 3 ft.

3 0
3 years ago
Find the area of the shaded region.
Sindrei [870]

Answer:

5x^2+28x+21

Step-by-step explanation:

  • First you want to find the area of the white rectangle
  • Then find the area of the beings rectangle
  • Then subtract beings minus white.

Hope it answers your question:)

5 0
3 years ago
Line WX and line YZ intersect at point V. If angle WVY = 4a + 58 and angle XVY = 2b - 18, find the values of a and b so that lin
amid [387]

we know that

If line WX is perpendicular to line YZ

then

see the attached figure to better understand the problem

m∠WVY=90°--------> 4a+58=90-----> 4a=90-58-----> a=32/4------> a=8°

m∠XVY=90°--------> 2b-18=90----> 2b=90+18------> b=118/2-------> b=59°

therefore

<u>the answer is</u>

a) The value of a is 8 degrees

b) The value of b is 59 degrees

5 0
3 years ago
The Sears Tower in Chicago is 1454 feet high. Sketch and find the angle of elevation from a point 750 feet from the base to the
liq [111]

Answer: A. 62.7

Step-by-step explanation:

Using the Pythagorean Theorem, know the distance from the top of the tower to the spot on the ground 750 feet away is 1636 feet.

Now with all lengths of the triangle we can solve for the angle giving us 62.7169723304

Now we round to the tenth as instructed and get an answer of 62.7

5 0
3 years ago
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