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3 years ago

Lesson 6.07

Mathematics

1 answer:

Oduvanchick [21]3 years ago

7 0

Answer:

A) Interval estimate for those that want to get out earlier = (35%) ± (4%) = (31%, 39%)

Interval estimate for those that want to get out later = (39%) ± (4%) = (35%, 43%)

B) The group that wants to get out of school earlier can win after all the votes are counted if their true population proportion takes on a value that is higher than the closest true population proportion (for the group that wants to get out of school later)

That is, in the (31%, 39%) and (35%, 43%) obtained in (a), a range of (35.1%, 39%) and (35%, 38.9%) show how possible that the group that wants to get out of school earlier can win after all the votes are counted.

Step-by-step explanation:

The Interval estimate for the a proportion is basically an interval of range of values where the true population proportion can be found with a certain level of confidence.

Mathematically,

Interval estimate = (Sample proportion) ± (Margin of error)

Margin of Error is the width of the confidence interval about the proportion.

a) Find the interval estimates

i) for those that want to get out earlier and

ii) those that want to get out later.

i) Sample proportion of those that want to get out earlier = 35%

Margin of Error = 4%

Interval estimate for those that want to get out earlier = (35%) ± (4%) = (31%, 39%)

ii) Sample proportion of those that want to get out later = 39%

Margin of Error = 4%

Interval estimate for those that want to get out later = (39%) ± (4%) = (35%, 43%)

b) Explain how it would be possible for the group that wants to get out of school earlier to win after all the votes are counted.

Since the interval estimates represent the range of values that the true population proportion can take on for each group that prefer a particular option, the group that wants to get out of school earlier van have their proportion take on values between 31% and 39%. If their true population takes on a value that is highest (which is very possible from the interval estimate), and the group with the highest proportion in the sample, (the group that wants to get out of school later, whose true population proportion can take between 35% and 43%) has a true population proportion that is less than that of the group that wants to get out of school earlier, then, the group that wants to get out of school earlier can win after all the votes are counted.

Hope this Helps!!!

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Answer:

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Sampling errors cannot be measured statistically.

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A sampling error can be described a the statistical error which do take place when an analyst does not select a sample which represents the entire population of data.

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In conclusion, Sampling errors cannot be measured statistically.

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1 year ago

Simplify. Rationalize the denominator. 9/ 5 + √3

salantis [7]

Step-by-step explanation:

To rationalize this, Multiply both numerator and denominator by the conjugate of the denominator

The conjugate of the denominator is 5-√3

9(5-√3)/(5+√3)(5-√3)

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3 years ago

Illinois license plates used to consist of either three letters followed by three digits or two letters followed by four digits.

n200080 [17]

Answer:

(a) 0.000028

(b) 0.002548

Step-by-step explanation:

First, we find the total number of plates possible by adding the numbers of the two types of plates.

1) 3 letters followed by 3 digits

number of plates of type 1) = 26^3 * 10^3 = 17,576,000

2) 2 letters followed by 4 digits

number of plates of type 2) = 26^2 * 10^4 = 6,760,000

Total number of plates = 17,576,000 + 6,760,000 = 24,336,000

(a) Only type 2) plates can have the number 8888.

With a fixed number part of 8888, there are 2 letter positions that cna have 26 different letters each.

Number of type 1) plates with the number part 8888

26^2 = 676

P(8888 in plate) = 676/24,336,000 = 0.000028

(b) The substring BE can appear in type 1) plates in 2 ways:

xBE or BEx

Since x above can be one of the 26 letters, and since the string of letters is followed by 3 digits, there are 26 * 1000, or 26,000 possible plates for xBE and another 26,000 possible plates for BEx.

The substring BE can appear in type 2) plates in only 1 way, BExxxx, where xxxx is 10,000 combinations of digits, so there are 10,000 possible type 2) plates with the substring BE.

Total number of type 1) and type 2) plates with substring BE is

26,000 + 26,000 + 10,000 = 62,000

p(substring BE) = 62,000/24,336,000 = 0.002548

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3 years ago

On the coordinate plane, point T is located at (0,7) and point U is located at (x,-5). The distance between points T and U is 15

yuradex [85]

Answer:

x = 9 or x = -9

Step-by-step explanation:

The parameters of the given points are;

The location of the point T = (0, 7)

The location of the point U = (x, -5)

Then distance between points T and U = 15 units

The distance between points A and B, 'd', given their coordinates, A(x₁, y₁) and B(x₂, y₂) is found using the following formula;

$d=\sqrt{\left (y_{2}-y_{1} \right )^{2}+\left (x_{2}-x_{1} \right )^{2}}$

Therefore, for the given points, T(0, 7) and U(x, -5), we get;

$15 = \sqrt{\left ((-5) - 7 \right )^{2}+\left (x - 0 \right )^{2}}$

Squaring both sides, gives;

$15^2 = \left ((-5) - 7 \right )^{2}+\left (x - 0 \right )^{2}} = (-12)^2 + x^2$

∴ x² = 15² - (-12)² = 81 = 9²

x² = 9²

∴ x = ±√(9²) = ± 9

The possible values of <em>x </em> are x = 9 or x = -9

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