A recent survey by the American Accounting Association revealed 52% of accountants have the Certified Public Accounting (CPA) ce
1 answer:
The random variable is given as the number of accountants that posses the CPA certificate. This is based on the fact that N= 15 and P = 0.52.
<h3>What is a random variable?</h3>A random variable is a variable with an unknown value or a function that gives values to each of the results of an experiment.
<h3>How is the random variable distributed?</h3>The random variable are distributed binomially.
<h3>What is the probability five of the 15 accountants are CPAs? </h3>The probability that five of the 15 accountants are CPAs is 0.0741.
This is derived as follows:
P (x =5) =
= 0.52
= (1- 0.52)
= 0.07412836549
P(x=5) ≈ 0.0741
<h3>What is the probability seven or eight of the 15 accountants are CPAs? </h3>P (x = 7 or x = 8) =
P (x = 7) + P (x = 8)
= (0.52)⁷ (o.48)⁸ +
(0.52)⁸ (0.48)⁷
= 0.18642 + 0.20196
= 0.388
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Full Question:
A recent survey by the American Accounting Association revealed 52% of accountants have the Certified Public Accounting (CPA) certificate. Suppose we select a sample of 15 accountants.
a-1. What is the random variable?
a-2. How is the random variable distributed?
b. What is the probability five of the 15 accountants are CPAs? (Round your answer to 4 decimal places.)
c. What is the probability seven or eight of the 15 accountants are CPAs? (Round your answer to 4 decimal places.)
d. What is the mean of the distribution of “number of CPA’s among 15 accountants”? (Round your answer to 1 decimal place.)
e. What is the variance of the distribution of “number of CPA’s among 15 accountants”? (Round your answer to 3 decimal places.)
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The Angle HCA is equal to 52°. This is arrived at using the knowledge of the Total value of Angles in a Triangle and the Total Value of Angles in a Polygon.
<h3>What other principles were used to arrive at the answer?</h3>
The other principles of mathematics that were used to arrive at the above answer are:
- Total Angles on a straight line;
- Total Angles on a point; and
- Line segments.
Step 1 - Recall that we have been given Angles AHB and BAH to be 128° and 28° respectively.
We also know that:
- The sum of angles in a triangle is 180°;...................A
- The sum of angles on a straight line is 180°;.........B
- The sum of angles in a polygon is 360°; while.....C
- The total sum of angles at a point is 360°.............D
Since A...therefore:
When ∠AHB (128°) and ∠BAH are taken from 180° we have DBA = ∠28°.
By observation, we can deduce that ∠BDE, ∠CDH, ∠CEH and ∠AEH are all right-angled triangles.
Using the above, we are able to repeat this process of solving for each angle until we have ∠HCA.
To verify that our answer is correct, recall that sum of angles in a polygon is 360°
That means:
∠BDA + ∠DHE + ∠CEH + ∠HCA = 360°
That is, 90+ 128 + 90 + 52 = 360°
See attached images and;
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