Question

Suppose a survey reveals that 69% of Canadian workers say job stress causes frequent health problems. One in four said they expected to burn out on the job in the near future. Thirty-two percent said they thought seriously about quitting their job last year because of workplace stress. Forty-nine percent said they were required to work more than 40 hours a week very often or somewhat often.

a. Suppose a random sample of 10 Canadian workers is selected.

What is the probability that more than seven of them say job stress caused frequent health problems?

What is the expected number of workers who say job stress caused

b. Suppose a random sample of 15 Canadian workers is selected.

What is the expected number of these sampled workers who say they will burn out in the near future?

What is the probability that none of the workers say they will burn out in the near future?

c. Suppose a sample of seven workers is selected randomly.

What is the probability that all seven say they are used very often or somewhat often to work more than 40 hours a week?

Answer 1

Answer:

a)

Given,

sample n = 10

p = 0.69

q = 1 - p = 1 - 0.69 = 0.31

P(X >= 7) = 1 - P(X <= 7)

= 1 - [10C0*0.69^0*0.31^10 + 10C1*0.69^1*0.31^9 + 10C2*0.69^2*0.31^8 + 10C3*0.69^3*0.31^7 + 10C4*0.69^4*0.31^6 + 10C5*0.69^5*0.31^5 + 10C6*0.69^6*0.31^4 + 10C7*0.69^7*0.31^3]

= 1 - [0 + 0.0002 + 0.0018 + 0.0108 + 0.0422 + 0.1128 + 0.2093 + 0.2662]

= 1 - 0.6433

= 0.3567

E(X) = np = 10*0.69 = 6.9

b)

E(X) = np = 15*(1/3) = 5

Probability = (1 - 1/3)^15

= 0.0023

c)

Probability = 0.49^7

= 0.0068