Brent needs to paint a logo made using two right triangles. The dimensions of the logo are shown below. What is the difference b
etween the area of the large triangle and the area of the small triangle?
Two right triangles are attached along their longest side. The smaller triangle has height 6 cm and base 2 cm. The height of the larger triangle is 9 cm and its base is 5 cm.
which is right out of the four
4.5 cm2
8.5 cm2
16.5 cm2
33.0 cm2
Two right triangles are attached along their longest side. The smaller triangle has height 6 cm and base 2 cm. The height of the larger triangle is 9 cm and its base is 5 cm.
which is right out of the four
4.5 cm2
8.5 cm2
16.5 cm2
33.0 cm2
1 answer:
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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