2 answers:
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Given:
The equation is
To find:
The properties which is not used from the given options.
Solution:
We have,
Using Multiplication Property of Equality, multiply both sides by 2.
(Distributive Property)
Using Subtraction Property of Equality, subtract 6n from both sides.
From the given options only one property is not used, i.e., Zero Product Property.
Therefore, the correct option is D.
Answer:
0.7123 = 71.23% probability that a random sample of 75 detached houses in Franklin County had a mean price greater than $190,000 in 2009.
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 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.
The mean price for a detached house in Franklin County, OH in 2009 was $192,723. Suppose we know that the standard deviation was $42,000.
This means that
Sample of 75:
This means that
What is the probability that a random sample of 75 detached houses in Franklin County had a mean price greater than $190,000 in 2009?
1 subtracted by the p-value of Z when X = 190000. So
By the Central Limit Theorem
has a p-value of 0.2877
1 - 0.2877 = 0.7123
0.7123 = 71.23% probability that a random sample of 75 detached houses in Franklin County had a mean price greater than $190,000 in 2009.