Question

The average price for a gallon of gasoline in the United States is $3.74 and in Russia it is $3.4. 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 $3.65 per gallon (to 4 decimals)?

b. What percentage of the gas stations in Russia charge less than $3.65 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)?

Answer 1

a. What is the probability that a randomly selected gas station in the United States charges less than $3.65 per gallon (to 4 decimals)?

Unites States:

^{μ = 3.74;σ = 0.25; X = 3.65}

Z = (x - μ) / σ

Z = (3.65-3.74)/0.25 = -0.36

P(Z < -0.36) = 0.3594

so, P(x < 3.65) = 0.3594

b. What percentage of the gas stations in Russia charge less than $3.65 per gallon (to 2 decimals)?

^{μ = 3.40;σ = 0.20; X = 3.65}

Z = (x - μ) / σ

Z = (3.65-3.40)/0.20 = 1.25

P(Z < 1.25) = 0.89

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)?

^{μ = 3.40;σ = 0.20; X = 3.74}

Z = (x - μ) / σ

Z = (3.74-3.40)/0.20 = 1.70

P(Z < 1.70) = 0.9554

Find more than the mean price in the United States

=1 - 0.9554

=0.0446

The probability that a randomly selected gas station in Russia charges more than the mean price in the United States is 0.0446