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R.R. Jha, Bachelor's Degree

Category: Calculus and Above

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Experience: Math Expert

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Let us assume that the prices of regular unleaded gasoline

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Let us assume that the prices of regular unleaded gasoline across the nation are normally distributed with a mean of $3.60 and a standard deviation of $0.32.

Describe the shape and horizontal scaling on the graph of the distribution for the population of all regular unleaded gasoline prices (hereafter referred to simply as gas prices).

If all possible samples of size 16 from the population of these gas prices are drawn and the mean is found for each sample, describe the shape and horizontal scaling on the graph of the sampling distribution for these sample mean values as theorized by the Central Limit Theorem.

Find the probability that the price from a single randomly selected gas station will be more than $4.00. Based upon your results, would it be unusual to find an individual gas station where the price is more than $4.00?

Find the probability that the mean from 16 randomly selected gas stations will be more than $4.00. Based upon your results, would it be unusual to find a sample of 16 randomly selected gas stations where the average price is more than $4.00?

A survey of 210 registered voters revealed that 107 of them plan on voting for the incumbent. Find a 95% confidence interval for the proportion of all registered voters who plan on voting for the incumbent. Does it appear statistically valid to conclude that more than 50% of all registered voters plan on voting for the incumbent? Why or why not?

Suppose you want to estimate the percentage of registered voters who plan to vote for the incumbent and you want your estimate to be within 2 percentage points of the correct population measure, based upon a 95% confidence level. What minimum size sample is required? Assume that no estimate of "p-hat" is known.

This probability is found by looking up the normal probability table or by using statistical calculator. I used Microsoft Excel to find this, exact probability was something like 2.87 x 10^-7.

And I've updated the file with answers to your bonus question too. You may download it from same link above.