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nerd58
06.04.2020 •
Mathematics
An architect is looking at the blueprints of a house and sees that a certain door is 6 centimeters wide on the plans. The architect needs to know the actual width of the door. From the key the architect sees that 1 centimeter represents 6 inches. How wide will the actual door ?
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Ответ:
36 inches
Step-by-step explanation:
Since for the equation 1 centimeter makes 6 inches and the door is 6 centimeters.
Do 6 • 6 which equals 36.
So the actual width of the door is 36 Inches!
Hope this helps!
Ответ:
0.0076 = 0.76% probability that less than 48.3% say they will vote for the incumbent.
Step-by-step explanation:
To solve this question, we use the normal probability distribution and the central limit theorem.
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean
and standard deviation
, the z-score 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 p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem establishes 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 a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean
and standard deviation ![s = \sqrt{\frac{p(1-p)}{n}}](/tpl/images/1372/7393/73804.png)
The proportion of eligible voters in the next election who will vote for the incumbent is assumed to be 54%. Sample of 450 voters.
This means that![p = 0.54, s = \sqrt{\frac{0.54*0.46}{450}} = 0.0235](/tpl/images/1372/7393/257a8.png)
What is the probability that in a random sample of 450 voters, less than 48.3% say they will vote for the incumbent?
This is the p-value of Z when X = 0.483. So
By the Central Limit Theorem
0.0076 = 0.76% probability that less than 48.3% say they will vote for the incumbent.