Thirty percent of salespersons in ABC Ltd. are male. A random sample of 100 sale

Question

Thirty percent of salespersons in ABC Ltd. are male. A random sample of 100 salespersons is selected.

(a)        Which distribution does this scenario fit and why?                           (2 marks)

(b)       Define the variable of interest, X.                                                       (1 mark)

(c)        What are the possible values of X?                                                     (1 mark)

(d)       What is the expected number of males?                                              (1 mark)

(e)        What is the standard deviation of the number of males?                    (1 mark)

(f)        What is the probability that there are exactly 25 males in the sample? (3 marks)

(g)        What is the probability of getting less than 36 males?                       (5 marks)

Explanation / Answer

Here Pr(Male) = p = 0.30

sample size n = 100

(a) It fits Binomial distribution and it is because the probability of being a male for a random human is constant and sample size is also given.

(b) Here variable of interest, X is the number of males out of 100 salespersons.

(c) Possible values of X are from 0 to 100.

(d) Expected number of males = E(X) = 100 * 0.30 = 30

(e) StdEV(X) = sqrt (0.30 * 0.70 * 100) = 4.583

(f) Pr(X = 25) = BIN(X = 25 ; 100 ; 0.30) = 0.0496 [ By binomal c alculator]

(g) Pr(X < 36) = BIN (X < 36 ; 100 ; 0.30) = 0.8840 [ by binomial calculator]

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.