Question

The average price for a gallon of gasoline in the United States is and in Russia it is . Assume these averages are the population means in the two countries and that the probability distributions are normally distributed with a standard deviation of in the United States and a standard deviation of in Russia. a. What is the probability that a randomly selected gas station in the United States charges less than per gallon (to 4 decimals)

Answer 1

This question is incomplete

Complete Question

The average price for a gallon of gasoline in the United States is $3.73 and in Russia it is $3.40 (Bloomberg Businessweek, March 5–March 11, 2012). 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.

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)

Answer:

0.1788

Step-by-step explanation:

We solve this question using z score formula.

z = (x-μ)/σ,

where x is the raw score

μ is the population mean

σ is the population standard deviation.

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)

For the United States

x is the raw score = $3.50

μ is the population mean = Average price for a gallon of gasoline in the United States is $3.73

σ is the population standard deviation = standard deviation of $.25 in the United States = $0.25

z score = $3.50 - $3.73/$0.25

=-0.92

Determining the Probability value from Z-Table:

P(x ≤ 3.50) = P(x < 3.5) = P(z = -0.92)

= 0.17879

Approximately to 4 decimal places = 0.1788

Therefore, the probability that a randomly selected gas station in the United States charges less than $3.50 per gallon is 0.1788