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wlad13 [49]
3 years ago
6

A random sample of 77 fields of durum wheat has a mean yield of 27.427.4 bushels per acre and standard deviation of 5.755.75 bus

hels per acre. Determine the 99%99% confidence interval for the true mean yield. Assume the population is approximately normal. Step 1 of 2 : Find the critical value that should be used in constructing the confidence interval. Round your answer to three decimal
Mathematics
1 answer:
xz_007 [3.2K]3 years ago
5 0

Answer:

[ 21.79, 33.0 ]

Step-by-step explanation:

Given:

Sample size, n = 7

Sample mean, μ = 27.4

Standard deviation, σ = 5.75

Confidence level is 99%

also, population is normal i.e normally distributed

Thus,

Confidence interval = μ ± z\frac{\sigma}{\sqrt n}

For confidence level of 99%

z-value = 2.58

Therefore,

Lower limit of Confidence interval = μ - 2.58\times\frac{5.75}{\sqrt{7}}

or

Lower limit of Confidence interval = 27.4 - 2.58\times\frac{5.75}{\sqrt{7}}

or

Lower limit of Confidence interval = 21.79

Upper limit of Confidence interval = μ + 2.58\times\frac{5.75}{\sqrt{7}}

or

Upper limit of Confidence interval = 27.4 + 2.58\times\frac{5.75}{\sqrt{7}}

or

Upper limit of Confidence interval = 33.00

Hence, confidence interval = [ 21.79, 33.0 ]

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An observer on top of a 50-foot tall lighthouse sees a boat at a 7° angle of depression. To the nearest foot, how far is the boa
Yuri [45]

Answer:

407.22 foot is the boat from the base of the lighthouse

Step-by-step explanation:

Given the statement: An observer on top of a 50-foot tall lighthouse sees a boat at a 7° angle of depression.

Let x foot be the distance of the object(boat) from the base of the lighthouse

Angle of depression = 7^{\circ}

\angle CAB = \angle DCA = 7^{\circ}       [Alternate angle]

In triangle CAB:

To find AB = x foot.

Using tangent ratio:

\tan (\theta) = \frac{Opposite side}{Adjacent Base}

\tan (\angle CAB) = \frac{BC}{AB}

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\tan (7^{\circ}) = \frac{50}{x}

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5 0
3 years ago
Please help me with this translating trigonometry graphs question. Brainliest and Points Available.
andreev551 [17]

According with the definition of translation, we conclude that the equations of graphs M and N are m(x) = f(x - 5) and n(x) = f(x) - 2, respectively.

<h3>How to apply translations on a given function</h3>

<em>Rigid</em> transformations are transformation such that the <em>Euclidean</em> distance of every point of a function is conserved. Translations are a kind of <em>rigid</em> transformations and there are two basic forms of translations:

Horizontal translation

g(x) = f(x - k), k ∈ \mathbb {R}     (1)

Where the translation goes <em>rightwards</em> for k > 0.

Vertical translation

g(x) = f(x) + k, k ∈ \mathbb {R}     (2)

Where the translation goes <em>upwards</em> for k > 0.

According with the definition of translation, we conclude that the equations of graphs M and N are m(x) = f(x - 5) and n(x) = f(x) - 2, respectively.

To learn more on translations: brainly.com/question/17485121

#SPJ1

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