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

Answers: 3

Show answers

Answers

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

arithmetic sequence

step-by-step explanation:

given that a sequence has terms as

19, 15, 11,

this is represented on a graph

the pattern indicates that the sequence is an arithmetic sequence with i term

a=19 and common difference d =-4

any general term

$a_{n}=a+(n-1)d\\ =19-5(n-1)\\=24-5n$

thus the sequence is reduced by 4 for each successive term starting from 1 and nth term is

24-5n.

first negative term would start after 5th term

5th term =24-25< 0

from 5th term onwards the sequence would be negative.

Answer from: Quest

6 meters

step-by-step explanation:

Another question on Mathematics

Mathematics, 21.06.2019 19:00

Use the quadratic formula to solve the equation. if necessary, round to the nearest hundredth. x^2 - 8 = -6x a. –7.12, 1.12 b. 7.12, –1.12 c. 7.12, 1.12 d. –7.12, –1.12

Answers: 2

Answer

Mathematics, 21.06.2019 19:00

45 was divided by a power of ten to get 4.5. what power of ten was it divided by? people 4.5

Answers: 3

Answer

Mathematics, 21.06.2019 20:00

M the table below represents a linear function f(x) and the equation represents a function g(x): x f(x)−1 −50 −11 3g(x)g(x) = 2x − 7part a: write a sentence to compare the slope of the two functions and show the steps you used to determine the slope of f(x) and g(x). (6 points)part b: which function has a greater y-intercept? justify your answer. (4 points)

Answers: 3

Answer

Mathematics, 21.06.2019 20:00

Bring the fraction a/a-4 to a denominator of 16-a^2

Answers: 1

Answer

You know the right answer?

Assume that 40% of graduates come from University A and and earn salaries of 30,000 on average with...

Questions