Question

The average price for a gallon of gasoline in the country A is $3.71 and in country B it is $3.45. 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 country A and a standard deviation of $0.20 in country B. What is the probability that a randomly selected gas station in country A charges less than $3.50 per gallon?

Answer 1

0.200454

Explanation:

Average price for a gallon of gasoline in the country A,
`\mu_A` = $3.71

Average price for a gallon of gasoline in the country B
`\mu_A`= $3.45

Standard deviation in the country A = $0.25

Standard deviation in the country B = $0.20

Now,

z score for the critical value

z =
`\frac{(x-\mu_A)}{\textup{Standard deviation}}`

here,

critical value, x = $3.50 per gallon

Therefore,

z =
`\frac{\textup{(3.50-3.71)}}{\textup{0.25}}`

or

z = -0.84

Hence,

Probability that a randomly selected gas station in country A charges less than $3.50 per gallon

i.e P(z < - 0.92)

from z table, we get

P(z < - 0.92) = 0.200454