Question

Suppose that 50% of the subscribers of a cable television company watch the shopping channel at least once a week. The cable company is trying to decide whether to replace this channel with a new local station. A survey of 100 subscribers will be undertaken. The cable company has decided to keep the shopping channel if the sample proportion is greater than 0.5775.

What is the approximate probability that the cable company will keep the shopping channel, even though the true proportion who watch it is only 0.50? (Round your answer to four decimal places.)

P(p̂ > 0.5775) =

Water permeability of concrete can be measured by letting water flow across the surface and determining the amount lost (in inches per hour). Suppose that the permeability index x for a randomly selected concrete specimen is normally distributed with mean value 1,000 and standard deviation 150.

(a)

How likely is it that a single randomly selected specimen will have a permeability index between 850 and 1,300? (Round your answer to four decimal places.)

P(850 < x < 1,300) =

(b)

If the permeability index is to be determined for each specimen in a random sample of size 10, how likely is it that the sample mean permeability index will be as follows?

(i)

between 900 and 1,100 (Round your answer to four decimal places.)

P(900 < x < 1,100) =

(ii)

between 850 and 1,300 (Round your answer to four decimal places.)

P(850 < x < 1,300) =

Answer 1

R software z valuesZ value using statistical table