Write an expression having only two terms that is equivalent to 2x – 3. Explain how you wrote the expression and how you can che
2 answers:
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Answer:
- 71° and 71°.
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Step-by-step explanation:
The triangle having two sides equal along with one different side is called an isosceles triangle.
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- So, Let us assume the other sides (two equal sides) of the isosceles triangle as x. As the different side is already given in the question.
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We know that,
- The sum of all angles of a triangle is 180°
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So, According to the question :
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Therefore,
- The measure of the two other angles of the isosceles triangle are 71° and 71°.
Answer:
The probability that the mean life expectancy of the sample is less than X years is the p-value of , in which
is the mean life expectancy,
is the standard deviation and n is the size of the sample.
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 normal distributions can be solved using the z-score formula.
In a set with mean and standard deviation
, the z-score 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 p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem establishes 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.
We have:
Mean , standard deviation
.
Sample of size n:
This means that the z-score is now, by the Central Limit Theorem:
Find the probability that the mean life expectancy will be less than years.
The probability that the mean life expectancy of the sample is less than X years is the p-value of , in which
is the mean life expectancy,
is the standard deviation and n is the size of the sample.