1)

The arrival of trucks on a receiving dock is a Poisson process with a mean arrival rate of two per hour.

(a) Find the probability that exactly 6 trucks arrive in a two-hour period.

(b) Find the probability that the time between two successive arrivals will be more than 3 hours.

2)

Suppose we want to test the null hypothesis m = 80 against the alternative hypothesis m = 77 on the basis of a random sample of size n = 100. (Assume that the population standard deviation is s = 8.4.) The null hypothesis is rejected if the sample mean `x< 78; otherwise it is accepted. What is the probability of Type I error; the probability of Type II error?

3)

Inspecting LCD screens prior to their connection to the keyboard and electronic components of laptop computer, a quality control engineer detects 22, 23, 26, 20, 24, and 29 defectives in six production runs each of size 200. With what degree of confidence can we assert that true average number of defectives in a production run of size 200 will be between 19.66 and 28.34?

(Note that the sample size isn= 6.)

Can anyone help me with these 3 problems?

Thanks!