Question

The average price for a gallon of gasoline in the United States is 3.75 and in Russia it is 3.37. 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 ________ per gallon (to 4 decimals)? b. What percentage of the gas stations in Russia charge less than _____ 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

Answer:

Given data,

The data represents the average price for a gallon of gasoline in the United States is 3.75 and in Russia it is 3.37.

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).The probability that a randomly selected gas station in the United States charges less than $3.50 per gallon:

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

First, compute the z score then find probability based on standard normal table.

x=$ 3.50

For converts to

From the standard normal distribution table, the associated probability for the area to the left is shown below,

P(z<-0.96)=0.1685

0.1685 is the probability that a randomly selected gas station in the United States charges less than $3.50 per gallon.

(b).To find the percentage of the gas stations in Russia charge less than $ 3.50 per gallon:

The percentage of the gas stations in Russia charge less than $3.50 per gallon is,

First, compute the z score then find probability based on standard normal table.

x=$ 3.50

For converts to

From the standard normal distribution table, the associated probability for the area to the left is shown below,

P(z<0.65)=0.7422=74.22%

74.22% is the percentage of the gas stations in Russia charge less than $3.50 per gallon.

(c).To find the probability that a randomly selected gas station in Russia charged more than the mean price in the United States:

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

First, compute the z score then find probability based on standard normal table.

x=$ 3.75

For converts to

From the standard normal distribution table, the associated probability for the area to the left is shown below,

P(z>1.9)=1-(z<1.9)

=1-0.9713

=0.0287

0.0287 is the probability that a randomly selected gas station in Russia charged more than the mean price in the United States.