A research group is on a college campus and is conducting a survey regarding the coffee consumption of college students in Ameri
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Answer:
When Sum of square of two Sides is equal to square of third side of triangle.
Step-by-step explanation:
Given:
Three side length of triangle are given we need find the which value to substitute for a, b, c in Pythagoras theorem.
First we will find the squares of all length, then we will check which two square of side are equal to square of third side as per Pythagoras theorem.
Hence the two side would according be a and b and third side will become c.
For example if length of triangle is given as 6 cm, 8 cm and 10 cm.
We will first take square of all
Now we can see that
Now by Pythagoras theorem.
Hence we can say a = 6 cm, b = 8 cm, c= 10 cm
Answer:
95.64% probability that under 30% of the dogs are emotional support trained
Step-by-step explanation:
For each dog, there are only two possible outcomes. Either they have completed emotional support training, or they have not. So we use the binomial probability distribution to solve this problem.
However, we are working with samples that are considerably big. So i am going to aproximate this binomial distribution to the normal.
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
Can be approximated to a normal distribution, using the expected value and the standard deviation.
The expected value of the binomial distribution is:
The standard deviation of the binomial distribution is:
Normal probability distribution
Problems of normally distributed samples can be 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.
When we are approximating a binomial distribution to a normal one, we have that ,
.
In this problem, we have that:
What is the probability that under 30% of the dogs are emotional support trained?
30% of 100 is 0.3*100 = 30
So this is the pvalue of Z when X = 30.
has a pvalue of 0.9564.
So there is a 95.64% probability that under 30% of the dogs are emotional support trained