Question

With the growing emphasis on technology and the changing business environment, many workers are discovering that training such as re-education, skill development, and personal growth is of great assistance in the job marketplace. A Gallup survey found that 80% of Generation Xers considered the availability of company-sponsored training as a factor to weigh in taking a job. If 50 Generation Xers are randomly sampled, what is the probability that fewer than 35 consider the availability of company-sponsored training as a factor to weigh in taking a job? What is the expected number? What is the probability that between 42 and 47 (inclusive) consider the availability of company-sponsored training as a factor to weigh in taking a job?

Answer 1

n = number of generation Xers are randomly selected = 50

p = P ( Generation Xers considered the availability of company sponsored training as a factor to weigh in taking a job) = 0.80

Consider the random variable X as

X : Number of Generation Xers considered the availability of company sponsored training as a factor to weigh in taking a job

The probability distribution of random variable X is binomial with parameter n = 50 and p = 0.80

X ~ Bin ( n = 50, p = 0.80)

E(X) = np = 50 * 0.80 = 40 and Var(X) = n*p * (1-p) = 50 * 0.80 *0.20 = 8

SD(X) =sqrt(8) = 2.8284

Since n is large and p is not small.

Using Normal approximation to binomial distribution

Z = ( X- E(X) ) / SD(X) ~ N(0,1).

i) Required Probability = P ( X < 35 )

Using Normal approximation to binomial distribution

= P ( Z < -1.7678)

From normal probability table

P(Z < -1.7678) = 0.0386

P( Fewer than 35 considered the availability of company sponsored training as a factor to weigh in taking a job) = 0.0386

ii) Required Probability =

= P ( 0.7071 < Z < 2.4749)

= P ( Z < 2.4749) - P ( Z < 0.7071)

from normal probability table

= 0.9933 - 0.7602

=0.2331

P( between 42 and 47 (inclusive) considered the availability of company sponsored training as a factor to weigh in taking a job) = 0.2331