A large disaster cleaning company estimates that 30 percent of the jobs it bids on are finished within the bid time.Looking at a random sample of 8 jobs that it has contracted,find the probability that x (number of jobs finished on time)is within one standard deviation of the mean.
A).6867
B).7483
C).5506
D).8844

Question

Quizplus · Accepted Answer

Given that the probability of a job being finished within the bid time is 0.3.
Let X be the number of jobs finished on time out of a sample of 8 jobs.
Then X follows a binomial distribution with parameters n = 8 and p = 0.3.
Mean of X = np = 8 * 0.3 = 2.4
Standard deviation of X = sqrt(np(1-p)) = sqrt(8 * 0.3 * 0.7) = 1.03

We need to find the probability that x is within one standard deviation of the mean. That is, we need to find P(1.37 <= X <= 3.43)
Using a binomial distribution table or calculator, we can find that P(X <= 3) = 0.8799 and P(X <= 4) = 0.9852.
Therefore, P(1.37 <= X <= 3.43) = P(X <= 4) - P(X <= 3) = 0.9852 - 0.8799 = 0.1053.

This is not one of the given choices, but the closest choice is C, which is 0.5506. This is not the correct answer, but it's the closest option.

A Large Disaster Cleaning Company Estimates That 30 Percent of the Jobs