Pleas find the area of the composite figure using the image attatched. Thank you! PLEASE NO WEBSITE LINKS!
1 answer:
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Answer:
0.0119 = 1.19% probability that the sample mean would be less than 35.2 dollars if a sample of 77 5-gallon pails is randomly selected
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(which is the square root of the variance)
, 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 less than 35.2 dollars if a sample of 77 5-gallon pails is randomly selected?
This is the pvalue of Z when X = 35.2.
By the Central Limit Theorem
has a pvalue of 0.0119
0.0119 = 1.19% probability that the sample mean would be less than 35.2 dollars if a sample of 77 5-gallon pails is randomly selected
<span>Reading the solution, please, look on the picture)
Let the side of the square will be X meters. This means that S1=x^2 </span>meters ^2<span>
One side of </span>new rectangular garden will be 2x meters and another (x-3) meters. So S2=2x(x-3) meters ^2
According to the <span>data:
</span><span>S1*1.25=S2
</span>x^2*1.25=<span>2x(x-3)
</span>1.25*x^2=2x^2-6x
0.75x^2-6x=0
3x^2-24x=0
x^2-8x=0
x(x-8)=0
x=8 or x=0
But x>0!
So x = 8 meters
The next question is to find S2.
S2=2x(x-3)=2*8*5=80 meters ^ 2
Let the side of the square will be X meters. This means that S1=x^2 </span>meters ^2<span>
One side of </span>new rectangular garden will be 2x meters and another (x-3) meters. So S2=2x(x-3) meters ^2
According to the <span>data:
</span><span>S1*1.25=S2
</span>x^2*1.25=<span>2x(x-3)
</span>1.25*x^2=2x^2-6x
0.75x^2-6x=0
3x^2-24x=0
x^2-8x=0
x(x-8)=0
x=8 or x=0
But x>0!
So x = 8 meters
The next question is to find S2.
S2=2x(x-3)=2*8*5=80 meters ^ 2