The amount of gasoline G sold each month to customers at Bob's Exxon station in downtown Navasota is a random variable. This random variable G can be described as having a normal distribution with mean 2500 gallons and a standard deviation of 250 gallons (and there is no seasonal variation in sales). Exxon will give Bob an all-expense paid trip to College Station, including a free dinner at Burger King, if his station pumps more than 3000 gallons in any one month. Required:

What is the probability that Bob will win that wonderful trip on the basis of his gasoline sales this month?

The probability is

Step-by-step explanation:

Let's start by defining the random variable as :

'' The amount of gasoline sold each month to customers at Bob's Exxon station in downtown Navasota ''

Therefore, if is a continuous random variable that has a normal distribution, we write ~ ( μ , σ )

Where ''μ'' is the mean and ''σ'' is the standard deviation.

For the random variable we write :

~

We need to find

In order to calculate this, we are going to standardize the variable. This means, finding the equivalent probability in a normal random variable

~

We perform this because the random variable ~ is tabulated in any book or either you can find the table on Internet.

To standardize the variable we need to subtract the mean and then divide by the standard deviation ⇒

⇒ P[ (G - μ) / σ > ] ⇒

Because (G - μ) / σ  ~

Finally, ⇒ = 1 - Φ(2)

Where '' Ф(x) = '' represents the cumulative function of

Looking for  Φ(2) in any table,

≅ %2.28

We found out that the probability is

look at the picture.

y-intercept for the function on a picture is 4 → point (0, 4).

y-intercept for the function

is for x = 0. substitute:

y-intercept is 8 → point (0, 8).

i wish i could you, i have no idea how to answer this

step-by-step explanation: