BUSI 230 HW 7.4 The Central Limit Theorem for Proportions Assignment solutions complete answers
Just put your values given and automatically provide answers for you!
If is the sample size and is the number in the sample who have a certain characteristic, then is called the sample .
The probability distribution of is called a distribution.
Below, is the sample size, is the population proportion and is the sample proportion. Use the excel spread sheet to find the probability. Round the answer to at least four decimal places.
Coffee: The National Coffee Association reported that 65% of U.S. adults drink coffee daily. A random sample of 250 U.S. adults is selected. Round your answers to at least four decimal places as needed.
(a) Find the mean .
(b) Find the standard deviation .
(c) Find the probability that more than 68% of the sampled adults drink coffee daily.
(d) Find the probability that the proportion of the sampled adults who drink coffee daily is between 0.59 and 0.67.
(e) Find the probability that less than 66% of sampled adults drink coffee daily.
(f) Would it be unusual if less than 61% of the sampled adults drink coffee daily?
Smartphones: A poll agency reports that 64% of teenagers aged 12-17 own smartphones. A random sample of 65 teenagers is drawn. Round your answers to at least four decimal places as needed.
(a) Find the mean .
(b) Find the standard deviation .
(c) Find the probability that more than 66% of the sampled teenagers own a smartphone.
(d) Find the probability that the proportion of the sampled teenagers who own a smartphone is between 0.61 and 0.75.
(e) Find the probability that less than 75% of sampled teenagers own smartphones.
(f) Would it be unusual if less than 60% of the sampled teenagers owned smartphones?
Working two jobs: About 17% of employed adults in the United States held multiple jobs. A random sample of 50 employed adults is chosen. Use Excel as needed.
(a) Is it appropriate to use the normal approximation to find the probability that less than 6.9% of the individuals in the sample hold multiple jobs? If so, find the probability. If not, explain why not.
(b) A new sample of 115 employed adults is chosen. Find the probability that less than 6.9% of the individuals in this sample hold multiple jobs. Round the answer to at least four decimal places.
(c) Find the probability that more than 6.4% of the individuals in the sample of 115 hold multiple jobs. Round the answer to at least four decimal places.
(d) Find the probability that the proportion of individuals in the sample of 115 who hold multiple jobs is between 0.180 and 0.220. Round the answer to at least four decimal places.
(e) Would it be unusual if less than 15% of the individuals in the sample of 115 held multiple jobs? Round the answer to at least four decimal places.
