A history exam features five questions. Three of the questions are multiple-choice with four options each. The other two questio
1 answer:
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Answer:
<em>The height of the bullding is 717 ft</em>
Step-by-step explanation:
<u>Right Triangles</u>
The trigonometric ratios (sine, cosine, tangent, etc.) are defined as relations between the triangle's side lengths.
The tangent ratio for an internal angle A is:
The image below shows the situation where Ms. M wanted to estimate the height of the Republic Plaza building in downtown Denver.
The angle A is given by his phone's app as A= 82° and the distance from her location and the building is 100 ft. The angle formed by the building and the ground is 90°, thus the tangent ratio must be satisfied. The distance h is the opposite leg to angle A and 100 ft is the adjacent leg, thus:
Solving for h:
Computing:
h = 711.5 ft
We must add the height of Ms, M's eyes. The height of the building is
711.5 ft + 5 ft = 716.5 ft
The height of the building is 717 ft
Answer:
and if we round up to the nearest integer we got n =174
Step-by-step explanation:
Previous concepts
The central limit theorem states that "if we have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed. This will hold true regardless of whether the source population is normal or skewed, provided the sample size is sufficiently large".
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
Let X the random variable who represents the test score of a student taking his final examination. We know from the problem that the distribution for the random variable X is given by:
From the central limit theorem we know that the distribution for the sample mean is given by:
Solution to the problem
We want to find the value of n that satisfy this condition:
And we can use the z score formula given by:
And we have this:
And we can express this like this:
And by properties of the normal distribution we can express this like this:
If we solve for we got:
Now we can find a quantile on the normal standard distribution that accumulates 0.03 of the area on the left tail and this value is:
And using this we have this equality:
If we solve for we got:
And then and if we round up to the nearest integer we got n =174