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prohojiy [21]
2 years ago
9

Drawing tree diagrams. After taking a course on statistics, 88% of students can successfully construct tree diagrams. Of those w

ho can construct tree diagrams, 90% passed, while only 60% of those students who could not construct tree diagrams passed. a) Construct a tree diagram of this scenario. ? You can do it electronically using e.g. PowerPoint, or draw freehand and scan the image. b) Calculate the probability that a student is able to construct a tree diagram if it is known that he or she passed.

Business
1 answer:
Yuliya22 [10]2 years ago
4 0

Answer:

A. Check the image

B. The probability that a student is able to construct a tree diagram if it is known that he or she passed is 79.2%

Explanation:

a) A tree diagram is a tool that simplifies the distribution of probabilities. So we start making branches (lines) according to the probability of each succes to happen, so in this case we first divide the tree diagram between those who can construct tree diagrams that represent the 88% so it means it has a probability of 0.88 and those who can't construct tree diagrams, so if 88% can  just 12% can't construct tree diagrams that is a probability of 0.12.  This is the first part of the tree diagram.

After that tere is another condition that is passing so for those who construct it is the 90% (0.9 probability) for passing, so in this group it is just 10% (0.1 probability) that doesn't pass. Now for those who don't construct tree diagrams, 60% (0.6 probability) pass so 40% losses (0.4)

See in the diagram that if you add the numbers that compound each of the vertices the result is a 100% or 1.0 probability, this is what you have to take into account when you are constructing a tree diagram.

b) For calculating a probability after constructing the tree diagram you just need to multiply each of the factor in which you are interested. In this case:

Construct tree diagram X Pass = 0.88 x 0.9 = 0.792

So the probability for a student that can construct a tree diagram to pass is 0.792, now for having in percentage we just need to multiply by 100% then:

0.792 x 100 = 79.2%

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Answer:

The question is not complete, below is the complete question:

Suppose that you open a mutual fund account with a deposit of 500 dollars. 5 months later, the fund balance is 600 dollars, and you withdraw 216 dollars. A year after the account was opened, your balance is X dollars. If the dollar weighted and time weighted rates of return were the same, what is the rate of return? (Assume simple interest for the dollar weighted calculation.) Answer should be a percent!!!

Answer:

The rate of return is 48% on deposited fund.

Explanation:

The rate of return on investment is the percentage increase on an amount invested for a particular period of time, and to calculate this, we will use the simple interest formula:

I = P × R × T

Where:

P = principal = $500

R = rate in decimal ( %rate/100)

T = time = 5 months = 5/12 years

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∴ 100 = 500 × R/100 × 5/12

100 = \frac{2500R}{1200}

120,000 = 2500R

∴ R = 120,000 ÷ 2500 = 48%

Therefore rate of return (R) = 48%

For a clearer understanding of the concept of interests, let us calculate for the balance after one year (X) as shown below:

I = P×R×T

T = 1 because, X is the balance after one year.

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but we were told that $216 was withdrawn at 5 months, hence the balance after one year = 740 - 216 = $524

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