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

Answer:

0.200454

Step-by-step 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