Amy is 3 years older than her brother. Together, their ages are 14. Amy wrote the equation x+(x+3)=14 to represent the sum of th
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Answer:
96.49% probability that the mean rent is more than $1100
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
, 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 mean rent is more than $1100?
This is 1 subtracted by the pvalue of Z when X = 1100. So
By the Central Limit Theorem
has a pvalue of 0.0351
1 - 0.0351 = 0.9649
96.49% probability that the mean rent is more than $1100
Note: Actually, the division problem should be in reverse order. It should be given as ---------(i)
But according to the given problem (x + 1) / (x² + 3 x + 2).
Here, (x² + 3 x + 2) > (x + 1)
or, (x + 2) > 1
Concept: By using the property of division, if the numerator is less than the denominator then the quotient will always be 0 (zero)
Therefore the option (d) 0 will be the correct option.