To solve this problem you must apply the proccedure shown below:
1. You have that varies inversely with
and when
the value of
is
.
2. Therefore, you can write the following expression, where is the constant of proportionality:
3. Solve for the constant of proportionality and substitute the values to calculate it:
4. The equation is:
The answer is:
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
Answer:
Step-by-step explanation:
You need to draw a right triangle as the one attached, where is the angle of elevation from the fire to the top of the fire tower.
You need to use the Inverse trigonometric function Arctangent:
Observe the triangle. You can identify that:
Then, you can substitute values:
Finally, evaluating, you get that the angle of elevation from the fire to the top of the fire tower is the following:
Rounded to the the nearest tenth of a degree:
