Suppose f(x) = (5 – x)^3 and, g(x) = a + x^2, and f(g(x)) = (1 – x^2)^3. What is the value of a?
2 answers:
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Answer:
58.32% probability that a randomly selected application will report a GMAT score of less than 600
93.51% probability that a sample of 50 randomly selected applications will report an average GMAT score of less than 600
98.38% probability that a sample of 100 randomly selected applications will report an average GMAT score of less than 600
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 a randomly selected application will report a GMAT score of less than 600?
This is the pvalue of Z when X = 600. So
has a pvalue of 0.5832
58.32% probability that a randomly selected application will report a GMAT score of less than 600
What is the probability that a sample of 50 randomly selected applications will report an average GMAT score of less than 600?
Now we have
This is the pvalue of Z when X = 600. So
has a pvalue of 0.9351
93.51% probability that a sample of 50 randomly selected applications will report an average GMAT score of less than 600
What is the probability that a sample of 100 randomly selected applications will report an average GMAT score of less than 600?
Now we have
has a pvalue of 0.9838
98.38% probability that a sample of 100 randomly selected applications will report an average GMAT score of less than 600
Answer:
Option B. t=5/3w ;1/3
Step-by-step explanation:
We are told that varies Inversely with
thus generally speaking
∝
since they are inverted, <u>otherwise</u> if they were proportionally varied then
∝
. This means that there is a constant value (
) for which
is inversely proportional to
and can be mathematically expressed as:
Eqn. (1)
Now since we are given the values of and
, we can plug them in Eqn. (1) and find our constant of proportionality
as follow:
Now that we have our constant we can find the new value for the second value of
as follow:
Therefore based on the options give, we can see that Option B. is correct since
and for
, then