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Answer:
0.0268 = 2.68% probability that the sample average is greater than $229,500
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
When the distribution is normal, we use 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.
Single house:
The mean appraised value of a house in this subdivision for all houses is $228,000, with a standard deviation of $8,500, which means that
Sample:
Sample of 120, so, by the central limit theorem,
What is the probability that the sample average is greater than $229,500?
This is 1 subtracted by the pvalue of Z when X = 229.5. So
By the Central Limit Theorem
has a pvalue of 0.9732
1 - 0.9732 = 0.0268
0.0268 = 2.68% probability that the sample average is greater than $229,500
One sixth of the lions is the two male lions.
One sixth of x lions is 2 lions.
Multiply both sides by 6.
Answer: There are 12 lions in the zoo.
One sixth of x lions is 2 lions.
Multiply both sides by 6.
Answer: There are 12 lions in the zoo.
Answer:
y=x+2
Step-by-step explanation:
To write the equation for this line, we are going to use slope-intercept form, which is written as
y=mx+b.
Here are the meanings of each variable:
y= basically the "name" of the function and it always stays as y.
m= slope, which is rise over run.
x= variable that is always on the right of the slope and it always stays as x.
b= y-intercept, or the value that crosses the y-axis.
We will substitute numbers into the equation along the way. The first thing we will want to do is find b, which is the easiest.
The line crosses the y-axis at 2, so that is our value of b.
Our new equation is
y=mx+2.
Next, we will find the slope. The most efficient way of doing this is looking at the lowest point that is already provided, (3, -2), and finding a way to rise and run to the highest point, (0, 2).
If you look closely at the graph, we need to rise up 4 and run over -3 to get to the other point. Therefore, the slope is , and we can substitute it into our equation, which is completed and is now
y=x+2
I hope this helps you out!! Have an awesome day ^^