Question

Find the probability and interpret the results. If convenient, use technology to find the probability. During a certain week the mean price of gasoline was $2703 per gallon. A random sample of 34 gas stations is drawn from this population. What is the probability that the mean price for the sample was between 2682 and 2722 that week? assume σ =$0.041

Can you please explain me this math problem. I am having so much trouble and go step by step to help me with this math problem. Thank you.

Step 1

**Central Limit Theorem ****for mean****:**

If a random sample of size *n *is taken from a population having mean and standard deviation then, as the sample size increases, the sample mean approaches the normal distribution with mean and standard deviation σ/ sqrt(n).

Step 2

**Find the probability that the mean price for the sample was between 2,682 and 2,722:**

The mean price of the gasoline is $2,703*.*That is, *μ* = $2,703. * *Random samples of 34 (*n*) gas stations are drawn from the population. The population standard deviation is σ = $0.041. The random variable *X *denotes the price of the gasoline. By central limit theorem for mean, the mean price of the sample follows a normal distribution with mean μ = $2,703 and standard deviation 0.041/sqrt (34) = 0.007.Thus, the probability that the mean price for the sample was between 2,682 and 2,722 is calculated as follows:

Step 3

**Interpretation:**

The probability that mean price for the sample was between 2,682 and 2,722 is 1. Therefore event that means price for the sample was between 2,682 and 2,722 is a sure event. It is expected th...

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