Question

According to a national poll, 41% of American workers said that they were completely
satisfied with their job. Find the probability that in a random sample of 1140 American workers, the
proportion of workers who are completely satisfied with their current job is between 0.4 and 0.44.

Answer 1

Here according to national poll 41% of American workers said that they are completely satisfied with their job. Here the population proportion is 41%. We need to find the probability that in a random sample of 1140 American workers , the proportion of workers who completely satisfied with their current job in between 0.4 and 0.44.

Here to compute the probability for proportion we have to use sampling Distribution for proportion. TheUThe sample size is large enough to use normal approximation.

Using normal approximation we computed the probability of randomly selected American , the proportion of workers who completely satisfied with their current job in bet 0.4 and 0.44 is as below,

Thus,

Therefore, based on the information provided, it is concluded that P(0.4≤p^​≤0.44)=0.7352.

Therefore the probability of randomly selected American workers, the proportion of workers who completely satisfied with their current job in between 0.4 & 0.44 is 0.7352.

Thank you.