According to a survey by Accountemps, 48% of executives believe that employees a

Question

According to a survey by Accountemps, 48% of executives believe that employees are most productive on Tuesdays. Suppose 200 executives are randomly surveyed.

a) Describe the sample distribution of the sample proportion of executives who believe that employees are most productive on Tuesdays when 200 executives are randomly surveyed.

b) What is the probability that fewer than 90 of the 200 executives surveyed believe employees are most productive on Tuesdays?

c) What is the probability that more than 100 of the 200 executives surveyed believe employees are most productive on Tuesdays?

Explanation / Answer

Solution:- Given that, q = 1-p = 1-0.48 = 0.52, n = 200

a) np = 200*0.48 = 96

b) P(X < 90) = P(Z < (90-96)/sqrt(200*0.48*0.52))

= P(Z < -0.8492)

= 0.1977

c) P(X > 100) = P(Z > (100-96)/sqrt(200*0.48*0.52))

= P(Z > 0.5661)

= 0.2843

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

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