Answer:
<em>A is correct answer</em>
Step-by-step explanation:
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Jose buys a wooden board that is 5 3/4 feet long the cost of the board is 0.60 perfect including tax what is the total cost in d
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Answer:
68.76% probability that the sampling error made in estimating the mean weekly salary for all employees of the company by the mean of a random sample of weekly salaries of 50 employees will be at most $50
Step-by-step explanation:
To solve this question, we have to understand the normal probability distribution and the central limit theorem.
Normal probability distribution:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean and standard deviation
, the zscore of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central limit theorem:
The Central Limit Theorem estabilishes that, for a random variable X, with mean and standard deviation
, a large sample size can be approximated to a normal distribution with mean
and standard deviation, which is also called standard error
In this problem, we have that:
What is the probability that the sampling error made in estimating the mean weekly salary for all employees of the company by the mean of a random sample of weekly salaries of 50 employees will be at most $50
This is the pvalue of Z when X = 1000+50 = 1050 subtracted by the pvalue of Z when X = 1000-50 = 950. So
X = 1050
By the Central Limit Theorem
has a pvalue of 0.8438
X = 950
has a pvalue of 0.1562
0.8438 - 0.1562 = 0.6876
68.76% probability that the sampling error made in estimating the mean weekly salary for all employees of the company by the mean of a random sample of weekly salaries of 50 employees will be at most $50
The angle of depression from the aeroplane to the ground will be 30 degrees.
<h3>What is trigonometry?</h3>
Trigonometry is the branch of mathematics which set up a relationship between the sides and angle of the right-angle triangles.
Given that:-
- An aeroplane is flying at the height of 10 km above the ground the distance along the ground from the aeroplane to the airport is 10√3 km
The angle of depression will be calculated as the angle between the horizontal and the height of the plane as shown in the figure below.
As we know that the perpendicular theta is height and the base ratio is angle tan theta.
tanФ = Height / Base
tanФ = 10 / 10 √3
tanФ = 1 / √3
Ф = tan⁻¹( 1 / √3 ) = 30°
Therefore the angle of depression from the aeroplane to the ground will be 30 degrees.
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