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1 answer:
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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 A. (-1, 0)
Step-by-step explanation:
In the figure attached,
Circle O is a unit circle (having radius r = 1 unit)
If a point A with central angles = θ, is lying on the circle then the coordinates of the point A will be,
x = r.cosθ
x = 1.cosθ = cosθ
and y = r.sinθ
y = 1.sinθ = sinθ
Therefore, coordinates representing the point A will be (cosθ, sinθ).
As per question the given point A is lying at P (a point having central angle θ = 180°)
Coordinates of point P will be
(x', y') → (cos180°, sin180°)
→ (-1, 0)
Therefore, Option A will be the answer.
