The average price of a gallon of unleaded regular gasoline was reported to be $2.34 in Northern Kentucky use this price as a population mean population standard deviation is $.20. question. what is the probability that the mean price for a sample of 30 station is good then $.03 of the population mean?
http://davidmlane.com/hyperstat/z_table.html
Even though u shown me Damon but how would the formula be set up I just want to know for future reference
mean = 2.34
sd = .2
z = + or - .03/.2
look for probability of being within z = +/- .15 of mean
Soo Damon do I plug in the mean within the problem cause I'm still lost
Or Damon do I divide .03/2 to come up with -/+ answers?
Now Damon I figure out that soo now do I take the mean and the probability and divide that again?
To find the probability that the mean price for a sample of 30 stations is within $0.03 of the population mean, we can use the Central Limit Theorem and the normal distribution.
1. Determine the standard deviation of the sampling distribution:
The standard deviation of the sampling distribution is calculated using the formula:
Standard Deviation of Sampling Distribution (σ) = Population Standard Deviation / √(Sample Size)
In this case, the population standard deviation is given as $0.20, and the sample size is 30. Therefore, the standard deviation of the sampling distribution is:
σ = $0.20 / √(30)
2. Calculate the standard error of the sampling distribution:
The standard error is another term for the standard deviation of the sampling distribution.
Standard Error = Standard Deviation of Sampling Distribution
Therefore, the standard error is also $0.20 / √(30).
3. Find the z-score for the given value of $0.03 within the sampling distribution:
To find the z-score, we use the formula:
z = (X - μ) / σ
In this case, X (the given value) = $0.03, μ (mean) = $2.34, and σ (standard deviation) = $0.20 / √(30). Calculate the z-score.
4. Determine the probability using the standard normal distribution table:
Once you have the z-score, you can find the probability associated with that z-score using a standard normal distribution table.
Look up the z-score obtained in the table, and find the corresponding cumulative probability. This cumulative probability will give you the probability that the mean price for a sample of 30 stations is within $0.03 of the population mean.
Alternatively, you can use statistical software or an online calculator to directly calculate the probability based on the given parameters and the normal distribution.