△HFM∼△PST
1 answer:
Answer:
The perimeter of △HFM is 50.75 units
Step-by-step explanation:
<u><em>The correct picture of the question in the attached figure</em></u>
we know that
If two figures are similar, then the ratio of its corresponding sides is proportional, and this ratio is called the scale factor
we have
△HFM∼△PST ----> given problem
step 1
Find the scale factor
Let
z ----> the scale factor
substitute the given values
step 2
Find the perimeter of triangle PST
Remember that the perimeter of a triangle is the sum of its three length sides
step 3
Find the perimeter of triangle HFM
we know that
If two figures are similar, then the ratio of its perimeters is equal to the scale factor
so
The perimeter of triangle HFM is equal to the perimeter of triangle PST multiplied by the scale factor
so
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Answer:
0.0174 = 1.74% probability that the sample mean would be greater than 101.63 WPM
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
, 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 greater than 101.63 WPM?
This is 1 subtracted by the pvalue of Z when X = 101.63. So
By the Central Limit Theorem
has a pvalue of 0.9826.
1 - 0.9826 = 0.0174
0.0174 = 1.74% probability that the sample mean would be greater than 101.63 WPM