Write the gcf of: 14x* and 180xy
1 answer:
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Answer:
0.0119 = 1.19% probability that the sample mean would be less than 35.2 dollars if a sample of 77 5-gallon pails is randomly selected
Step-by-step explanation:
To solve this question, we need 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(which is the square root of the variance)
, 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 normally distributed random variable X, with mean and standard deviation
, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean
and standard deviation
.
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
In this problem, we have that:
What is the probability that the sample mean would be less than 35.2 dollars if a sample of 77 5-gallon pails is randomly selected?
This is the pvalue of Z when X = 35.2.
By the Central Limit Theorem
has a pvalue of 0.0119
0.0119 = 1.19% probability that the sample mean would be less than 35.2 dollars if a sample of 77 5-gallon pails is randomly selected
Answer: C. - √2
Step-by-step explanation:
<u>Given requirements from the question</u>
Find the exact value of sec 135°
<u>Convert into common trigonometric expression</u>
sec = secant
secx = 1 / cosx
Therefore, sec 135° = 1 / (cos 135°)
<u>Find the reference angle</u>
135° is quite a complicated angle, but it is possible to simplify it by finding its reference angle.
Since 135° is in the second quadrant, its reference angle will be
180° - 135° = 45°
However, we need to consider the positive and negative.
In a coordinate plane, the clue is (A S T C), which corresponds to the positive values in each quadrant. In the QI, "All" are positive. In the QII, sine is positive. In the QIII, the tangent is positive. In QIV, cosine is positive.
Therefore, when the value of cosine is in QII, it is negative.
The reference angle = - (1 / cos 45°)
<u>Determine the final value</u>
Given that the reference angle = - (1 / cos 45°)
cos 45° = 1 / √2
Therefore:
sec 135° = - (1 / cos 45°) = - (1 / (1 / √2)) =
Hope this helps!! :)
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