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Suppose that the average price for a gallon of gasoline in the United States is $3.76 and in Russia it is $3.39. Assume these averages are the population means in the two countries and that the probability distributions are normally distributed with a standard deviation of $0.25 in the United States and a standard deviation of $0.20 in Russia. a. What is the probability that a randomly selected gas station in the United States charges less than $3.50 per gallon (to 4 decimals)? b. What percentage of the gas stations in Russia charge less than $3.50 per gallon (to 2 decimals)? c. What is the probability that a randomly selected gas station in Russia charged more than the mean price in the United States (to 4 decimals)?

          Suppose that the average price for a gallon of gasoline in the United States is $3.76 and in Russia it is $3.39. Assume these averages are the population means in the two countries and that the probability distributions are normally distributed with a standard deviation of $0.25 in the United States and a standard deviation of $0.20 in Russia.
a. What is the probability that a randomly selected gas station in the United States charges less than $3.50 per gallon (to 4 decimals)?
b. What percentage of the gas stations in Russia charge less than $3.50 per gallon (to 2 decimals)?
c. What is the probability that a randomly selected gas station in Russia charged more than the mean price in the United States (to 4 decimals)?

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Suppose that the average price for a gallon of gasoline in the United States is 3.76 and in Russia it is3.39. Assume these averages are the population means in the two countries and that the probability distributions are normally distributed with a standard deviation of 0.25 in the United States and a standard deviation of0.20 in Russia.
a. What is the probability that a randomly selected gas station in the United States charges less than 3.50 per gallon (to 4 decimals)?
b. What percentage of the gas stations in Russia charge less than3.50 per gallon (to 2 decimals)?
c. What is the probability that a randomly selected gas station in Russia charged more than the mean price in the United States (to 4 decimals)?

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Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

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Solved by Expert Katy Gimbel

02/28/2022

Step 1

50 per gallon, we need to calculate the z-score. The z-score is calculated by subtracting the mean from the value and dividing by the standard deviation. However, since the average price for a gallon of gasoline in the United States is $3.76, it is clear that the Show more…

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Suppose that the average price for a gallon of gasoline in the United States is $3.76 and in Russia it is $3.39. Assume these averages are the population means in the two countries and that the probability distributions are normally distributed with a standard deviation of $0.25 in the United States and a standard deviation of $0.20 in Russia. a. What is the probability that a randomly selected gas station in the United States charges less than $3.50 per gallon (to 4 decimals)? b. What percentage of the gas stations in Russia charge less than $3.50 per gallon (to 2 decimals)? c. What is the probability that a randomly selected gas station in Russia charged more than the mean price in the United States (to 4 decimals)?

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00:02 This question involves a series of questions involving gas prices.

00:08 It says we're told that in the united states, gas prices follow normal distribution with a mean of 3 .76 and a standard deviation of 0 .25.

00:19 And in russia, we're told that gas prices also follow an approximately normal distribution with mean 3 .39 and standard deviation of 0 .20.

00:29 So the first thing we want to know is what is the probability that.

00:33 In the u .s.

00:35 We're being charged less than $3 .50.

00:41 And we're going to round this to four decimals.

00:45 So if we look at a normal distribution, 376 is in our middle, 350 is over here, and we're finding the area to the left of that.

00:55 So the probability that x is less than 350.

01:00 So using our graphing calculators, we're going to use our normal cdf.

01:09 Our lower bound is negative 99999.

01:14 Our upper bound is 350.

01:17 Our mean is 3 .76.

01:21 And our standard deviation is 0 .25.

01:24 That tells us that the probability that it is less than $3 .50 is 0 .1492.

01:32 Part b said what percent of gas in russia is more than 350.

01:40 So we know the probability that x is greater than 350, but this is for russia...

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