he Oil Price Information Center reports the mean price per gallon of regular gasoline is $ 3.79 with a population standard deviation of $ 0.18.
Assume a random sample of 40 gasoline stations is selected and their mean cost for regular gasoline is computed.
1. What is the population in this case? what is the sample? what is the sample size?
2. What is the standard error of the mean in this experiment?
3. What is the probability that the sample mean is between $ 3.77 and $ 3.81?
4. What is the probability that the difference between the sample mean and the population mean is less than 0.01?
5. What is the likelihood the sample mean is greater than $ 3.87?
2.0285
1. In this case, the population refers to all gasoline stations. The sample is a subset of the population, consisting of 40 randomly selected gasoline stations. The sample size is 40.
2. The standard error of the mean (SEM) in this experiment can be calculated using the formula:
SEM = (Population Standard Deviation) / √(Sample Size)
Given that the population standard deviation is $0.18 and the sample size is 40, we can substitute these values into the formula to find the standard error of the mean:
SEM = $0.18 / √(40)
By calculating this expression, we can determine the standard error of the mean.
3. To find the probability that the sample mean is between $3.77 and $3.81, we need to use the concept of the standard normal distribution. We can assume that the sample mean follows a normal distribution due to the Central Limit Theorem.
First, we need to convert the given sample mean values into z-scores using the formula:
z = (sample mean - population mean) / (standard deviation / √sample size)
By substituting the given values into this formula, we can find the z-scores for both $3.77 and $3.81.
Next, we can use a standard normal distribution table or a calculator to find the probabilities associated with these z-scores. Finally, subtract the probability corresponding to $3.77 from the probability corresponding to $3.81 to get the probability that the sample mean is between $3.77 and $3.81.
4. To find the probability that the difference between the sample mean and the population mean is less than 0.01, we need to calculate the z-score using the formula from the previous question. The difference between the sample mean and the population mean is 0.01, and we need to find the probability associated with this z-score using the standard normal distribution table or calculator.
5. To determine the likelihood that the sample mean is greater than $3.87, we need to compute the z-score using the formula mentioned earlier. Next, we use a standard normal distribution table or calculator to find the probability associated with this z-score. The probability obtained represents the likelihood that the sample mean is greater than $3.87.