The amount of time adults spend watching television is closely monitored by firms because this helps to determi advertising pricing for commercials. Complete parts (a) through (d).
Interpret this probability. Select the correct choice below and fill in the answer box within your choice.
(Round to the nearest integer as needed)
A. If 1000 different random samples of size $n=45$ individuals from a population whose mean is assumed to be 2.35 hours is obtained, we would expect a sample mean of exactly 1.98 in about of the samples.
B. If 1000 different random samples of size $n=45$ individuals from a population whose mean is assumed to be 2.35 hours is obtained, we would expect a sample mean of 1.98 or more in about $=$ of the samples.
If 1000 different random samples of size $n=45$ individuals from a population whose mean is assumed to be 2.35 hours is obtained, we would expect a sample mean of 1.98 or less in about 99 of the samples.
Based on the result obtained, do you think avid Internet users watch less television?
Yes
No
Answer
Final Answer: If 1000 different random samples of size \(n=45\) individuals from a population whose mean is assumed to be 2.35 hours is obtained, we would expect a sample mean of 1.98 or less in about \(\boxed{145}\) of the samples.
Step 1 ：The question is asking to interpret the probability of obtaining a sample mean of 1.98 hours from a population whose mean is assumed to be 2.35 hours. The sample size is 45 individuals and we are considering 1000 different random samples.
Step 2 ：To solve this, we need to calculate the z-score for the sample mean of 1.98 hours. The z-score is a measure of how many standard deviations an element is from the mean. In this case, it will tell us how many standard deviations the sample mean of 1.98 hours is from the population mean of 2.35 hours.
Step 3 ：Once we have the z-score, we can use it to find the probability of obtaining a sample mean of 1.98 hours or less. This probability will tell us how many out of 1000 samples we would expect to have a sample mean of 1.98 hours or less.
Step 4 ：Using the given values, we find that the z-score is approximately -1.056 and the probability is approximately 0.145.
Step 5 ：Multiplying this probability by the number of samples (1000), we find that we would expect about 145 of the samples to have a sample mean of 1.98 hours or less.
Step 6 ：Final Answer: If 1000 different random samples of size \(n=45\) individuals from a population whose mean is assumed to be 2.35 hours is obtained, we would expect a sample mean of 1.98 or less in about \(\boxed{145}\) of the samples.
