Question

The age distribution for the employees of a highly successful “start-up” company head-quarted in Jakarta is shown in the following data. Age 20 21 22 23 24 25 26 27 28 29 30 31 32 33 Proportion 0.02 0.04 0.05 0.07 0.04 0.02 0.07 0.02 0.11 0.07 0.09 0.13 0.15 0.12 An employee is to be randomly selected from this population.

a. Can the relative frequency distribution in the table be interpreted as a probability distribution? Explain.

b. Graph the probability distribution.

c. What is the probability that the randomly selected employee is under 30 years old?

d. What is the probability that the randomly selected employee is over 40 years old?

e. What is the probability that the randomly selected employee will be between 25 to 30 years old?

Answer 1

(A) 0.02+ 0.04 +0.05+ 0.07+ 0.04 +0.02 +0.07+ 0.02+ 0.11+ 0.07+ 0.09+ 0.13+ 0.15 +0.12 = 1

yes, the relative frequency distribution in the table can be interpreted as a probability distribution because the total sum of all the given probability is equal to 1

(B) Using excel, select the data, click on insert tab, select scatter plot

(C)  probability that the randomly selected employee is under 30 years old = sum of all probability till x = 29

P(under 30) = P(x=20)+P(x=21)+P(x=22)+P(x=23)+P(x=24)+P(x=25)+P(x=26)+P(x=27)+P(x=28)+P(x=29)

using the probability distribution table

= 0.02+ 0.04 +0.05+ 0.07+ 0.04 +0.02 +0.07+ 0.02+ 0.11+ 0.07

= 0.51

(D) probability that the randomly selected employee is over 40 years old = 0 because probability distribution is limited till 33 years.

(E) probability that the randomly selected employee will be between 25 to 30 years old = P(25<x<30)

= P(26 to 29)

= P(x=26)+P(x=27)+P(x=28)+P(x=29)

using the probability distribution table

= 0.07 +0.02+ 0.11 + 0.07

= 0.27