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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.)