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 $.25 in the United States and a standard deviation of $.20 in Russia. What percentage of the gas stations in Russia charge less than $3.50 per gallon (to 2 decimals)?

Question

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 $.25 in the United States and a standard deviation of $.20 in Russia.  What percentage of the gas stations in Russia charge less than $3.50  per gallon (to 2 decimals)?

Louis Smith · Accepted Answer

Step 1  The Z-score of a random variable X is defined as follows:  Z=X–μσ.  Here, μ and σ are the mean and standard deviation of X, respectively.  Step 2  Consider a random variable X that defines the price for a gallon of gasoline in Country R.  According to the given information X follows normal distribution with mean $3.39 and standard deviation of $0.20.  The probability of the gas stations in Country R charge is less than $3.50 per gallon is,  P(X&amp;lt;3.50)=P(X−μσ&amp;lt;3.50−3.390.20)  =P(Z&amp;lt;0.55)  =0.7088 [using the standard normal table or using the Excel formula =NORM.S.DIST(0.55, TRUE)]  Therefore, 70.88% of the gas stations in Country R charge is less than $3.50 per gallon.

The average price for a gallon of gasoline in the United States is $3.

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