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?

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valetta valetta · Answer 1 · 2019-11-04T08:53:45+01:00

Answer:

0.200454

Step-by-step explanation:

Average price for a gallon of gasoline in the country A, [tex]\mu_A[/tex] = $3.71

Average price for a gallon of gasoline in the country B [tex]\mu_A[/tex]= $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 = [tex]\frac{(x-\mu_A)}{\textup{Standard deviation}}[/tex]

here,

critical value, x = $3.50 per gallon

Therefore,

z = [tex]\frac{\textup{(3.50-3.71)}}{\textup{0.25}}[/tex]

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