Mathematics, 21.04.2020 21:48 adammouedden198

Assume that 40% of graduates come from University A and and earn salaries of 30,000 on average with a standard deviation of 5,000. The remainder come from University B and earn salaries of 25,000 on average with a standard deviation of 7,500. If you are told that a graduate is earning less than 35,000, what is the probability that they came from University A

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Answer from: sloane50

38.18% probability that they came from University A

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the conditional probability formula.

Normal probability distribution:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

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.

Conditional probability formula:

We use the conditional probability formula to solve this question. It is

$P(B|A) = \frac{P(A \cap B)}{P(A)}$

In which

P(B|A) is the probability of event B happening, given that A happened.

$P(A \cap B)$ is the probability of both A and B happening.

P(A) is the probability of A happening.

If you are told that a graduate is earning less than 35,000, what is the probability that they came from University A

So:

Event A: earning less than 35,000

Event B: coming form university A.

Probability of earning less than 35,000.

40% come from University A.

University A: Mean 30,000 and standard deviation 5,000.

This probability is the pvalue of Z when X = 35,000. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{35,000 - 30,000}{5,000}$

Z = 1

Z = 1 has a pvalue of 0.8413.

Intersection is coming from university A and earning less than 35,000. So

$P(A \cap B) = 0.40*0.8413 = 0.33652$

60% come from university B:

Mean 25,000 and standard deviation 7,5000.

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{35,000 - 25,000}{7,500}$

Z = 1.33

Z = 1.33 has a pvalue of 0.9082.

Then

P(A) = 0.40*0.8413 + 0.6*0.9082 = 0.88144

Finally:

$P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.33652}{0.88144} = 0.3818$

38.18% probability that they came from University A

Answer from: Quest

Istg idk..if there all the same length there all the same number but use google
How do you find the area of similar figures given a side length?

Answer from: Quest

it is contrapositive

i could not see the question too well so check yourself again too . this is because i want you to get it correct.

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