According to the American Automobile Association, the average cost of a gallon of regular unleaded fuel at gas stations in January 2019 was $3.5. Assume that the standard deviation of such costs was $4.75. Suppose that a random sample of 56 gas stations was selected from the population and the cost per gallon of regular unleaded fuel was determined for each gas station. Consider X¯bar, the sample mean cost per gallon. (a) Describe the sampling distribution of X¯bar. (b)Find the probability that the sample had a mean fuel cost between $3.8 and $4. (c) How would the sampling distribution of X¯bar change if the sample size were doubled?

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A: The required Percentage is, 3.6%  the detailed solution is as follows below:

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A:

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A:

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A: Given that  X~N( μ = 65 , ? = 5 ) μ = 55 , ? = 5

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A: X follows a Normal distribution with mean = 24 and S.D = 6 Then z=(x-mean)/SD = (x-24)/6  follows…

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A: Given that.   X~N( μ , ?)   μ=64.7     , ?=3.1   Z-score =( x - μ )/?

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A: Let p be the population proportion of successes.

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A: Using Excel>data>data analysis>ANOVA>One-way ANOVA, we get: Since, P-value < 0.05 OR…

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A:

Q: Can the standard deviation of a data set be zero

A: Standard deviation can not be negative.

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A: Given data N = 36 SD = 221.6

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A: It is given that the average wage of plumbers is normally distributed with a mean of $20 and a…

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A: It is given that, Mean =24.1  Median =26.4

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.