The sum of 3x^2+4x-2 and x^2-5x+3 is
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Answer:
11.51% probability that it will take less than 450 days to train all the contestants.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
When the distribution is normal, we use 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 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.
For the sum of n variables, the mean is and the standard deviation is
In this question:
Approximate the probability that it will take less than 450 days to train all the contestants.
This is the pvalue of Z when X = 450.
By the Central Limit Theorem
has a pvalue of 0.1151
11.51% probability that it will take less than 450 days to train all the contestants.
We have been given a chord and tangent to a circle. We have been minor arc measure that is equal to .
Since we know that angle formed by a secant and tangent of circle is half of the measure of intercepted arc.
We can find intercepted arc by subtracting minor arc measure from 360 degrees because minor and major arcs add up to 360 degrees.
Now we will plug given values in our formula,
Therefore, the measure of d is 121 degrees.