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.

Answer 1

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.

What is a random variable?

A random variable is a variable with an unknown value or a function that gives values to each of the results of an experiment.

How is the random variable distributed?

The random variable are distributed binomially.

What is the probability five of the 15 accountants are CPAs?

The probability that  five of the 15 accountants are CPAs is 0.0741.

This is derived as follows:

P (x =5) = $C^{15} _{5}$

= 0.52$^{5}$

= (1- 0.52)$^{15-5}$

= 0.07412836549

P(x=5) ≈ 0.0741

What is the probability seven or eight of the 15 accountants are CPAs?

P (x = 7 or x = 8) =

P (x = 7) + P (x = 8)

= $C^{15} _{7}$ (0.52)⁷ (o.48)⁸ + $C^{15} _{8}$ (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.)