Question

Assume that 25 percent of all business executives feel that the benefits of outsourcing are either less or much less than expected. What is the probability of observing a random sample of 1,000 randomly selected business executives with a sample proportion of 22 percent?

Answer 1

probability = 0.0026

Explanation:

given data

random sample n = 1,000

benefits of outsourcing p = 25 percent

sample proportion = 22 percent

solution

we know here

p = 0.25

and P(p1 = 0.22)

so P( X = 220)

and

P(219.5 < X < 220.5)

and here mean will be

mean = n × p

mean = 1000 × 0.25

mean = 250

and standard deviation will be

standard deviation SD =
`√((npq))`

SD =
`√((1000* 0.25* 0.75))`

SD = 13.6930

and we know Z is

Z =
`((X - mean))/(SD)`

so here

P(219.5 < X < 220.5)

probability = 0.0026