Question

According to a survey, 63% of young Americans aged 18 to 29 say the primary way they watch television is through streaming services on the Internet. Suppose a random sample of 150 Americans from this age group is selected Complete parts (a) through (d) below. b. Verify that the conditions for the Central Limit Theorem are met. The Random and Independent condition holds assuming independence. The Large Samples condition holds. The Big Populations condition can reasonably be assumed to hold c. Would it be surprising to find that 99 people in the sample watched television primarily through streaming services? Why or why not? Select the correct choice below and fill in the answer box within your choice. (Type an integer or decimal rounded to two decimal places as needed) O A. With a 2-score of it would be surprising because this 2-score is small OB. With a z-score of it would not be surprising because this 2-score is small OC. With a z-score of it would not be surprising because this 2-score is large OD. With a z-score of it would be surprising because this z score is large. ! T va Vo (1.0) I.

Answer 1

The conditions for the Central Limit Theorem are met in this case. The probability of finding 99 people in the sample who watch television primarily through streaming services cannot be determined without the standard deviation.

To verify that the conditions for the Central Limit Theorem (CLT) are met, we need to check the three conditions:

1. Random and Independent condition: As long as the sample is randomly selected and the individuals in the sample are independent of each other, this condition is satisfied.
2. Large Samples condition: The sample size of 150 is considered large enough for the CLT to be applicable.
3. Big Populations condition: The question assumes that the population of young Americans aged 18 to 29 is sufficiently large, so this condition can be reasonably assumed to hold.

Therefore, all the conditions for the Central Limit Theorem are met in this case.

Regarding the probability of finding 99 people in the sample who watch television primarily through streaming services, we can use the Central Limit Theorem to approximate the probability. We can calculate the z-score and compare it to a standard normal distribution to determine if it is surprising or not.

The z-score is calculated as z = (x - μ) / σ, where x is the observed value, μ is the expected value, and σ is the standard deviation. In this case, x = 99, μ = 63, and we don't have the standard deviation. Without the standard deviation, we cannot calculate the z-score, and therefore, we cannot determine if it would be surprising or not.