Q 1.46. - Elementary Statistics

Question

Best-Selling Albums. Refer to Exercise 1.44. 

(a) List the 20 possible samples (without replacement) of three artists that can be selected from the six. 

(b) Describe a procedure for taking a simple random sample of three artists from the six.

(c) If a simple random sampling procedure is used to obtain three artists, what are the chances of selecting M, A, and L? P, L, and E?

Step-by-Step Solution

Answer

Part (a)  (E, M, P), (E, M, L), (E, M, A), (E, M, B), (E, P, L), (E, P, A), (E, P, B), (E, L, A ), (E, L, B), (E, A, B), (M, P, L), (M, P, A), (M, P, B), (M, L, A), (M, L, B) (M, A, B), (PLA), (PLB),

(P, A, B), (L, A, B)

Part (b)  Use the procedure of simple random sampling.

Part (c) $\frac{1}{20}$for each.

Part(a) Step 1. Given information.

The given statement is:

From exercise 1.44 we know that Eagles (E), Michael Jackson (M), Pink Floyd (P), Led Zeppelin (L), AC/DC (A), and Billy Joel (B) are the top six best-selling albums by artist (B).

Part (a) Step 2. List the 20 possible samples (without replacement) of three artists that can be selected from the six.

Samples are: 

(E, M, P), (E, M, L), (E, M, A), (E, M, B), (E, P, L), (E, P, A), (E, P, B), (E, L, A ), (E, L, B), (E, A, B), (M, P, L), (M, P, A), (M, P, B), (M, L, A), (M, L, B) (M, A, B), (PLA), (PLB),

(P, A, B), (L, A, B)

Part (b) Step 1. Describe the procedure of selecting the random sample.

We can follow the below-given procedure for taking a random sample:

1. We can write the letters that correspond to the six best-selling albums of all time (E, M, P, L, A, B) on separate pieces of paper to produce a simple random sample of size 3.
2.  We could choose three slips of paper while blindfolded by placing these six slips of paper in a box and shaking it.

Part (c) Step 1. Find the probability of selecting (M, A, and L) and (P, L, and E).

Total outcomes are 20.

The probability of selecting M, A, and L is:

$=\frac{1}{20}$

 The probability of selecting P, L, and E is:

$=\frac{1}{20}$