A bag contains colored tiles 6 tiles are green 3 tiles are blue 3 tiles are red a tile will be randomly selected from the bag. W
2 answers:
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Probabilities are used to determine the chances of events
The given parameters are:
- Sample size: n = 20
- Proportion: p = 85%
Using the binomial probability formula, we have:
So, the equation becomes
This gives
Express as percentage
Hence, the probability that 11 out of the 20 would graduate is 0.11%
<h3>(b) To what extent do you think the university’s claim is true?</h3>The probability 0.11% is less than 50%.
Hence, the extent that the university’s claim is true is very low
<h3>(c) What is the probability that all 20 would graduate? </h3>Using the binomial probability formula, we have:
So, the equation becomes
This gives
Express as percentage
Hence, the probability that all 20 would graduate is 3.88%
<h3>(d) The mean and the standard deviation</h3>The mean is calculated as:
So, we have:
The standard deviation is calculated as:
So, we have:
Hence, the mean and the standard deviation are 17 and 2.55, respectively.
Read more about probabilities at:
Angles ∠ACD and ∠CAB are congruent because they are alternate angles. Then the area of the triangle AOB will be 22.53 square cm.
<h3>What is the area of the right-angle triangle?</h3>The area of the right-angle triangle is given as
A = 1/2 x B x H
Where B is the base and H is the height of the right triangle.
We know that angles ∠ACD and ∠CAB are congruent because they are alternate angles.
α₁ = 40°
AO = OC = 7.8 cm
Then the area of the triangle will be
Area = 1/2 x 7.8 x 7.8 x tan40°
Area = 22.53 square cm
More about the area of the right-angle triangle link is given below.
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