the amount of gas in sarahs car is uniformly distributed between 1 and 16 gallons. Calculate the probability that the amount of gas is exactly 7 gallons

The probability that the amount of gas in Sarah's car is exactly 7 gallons is 0.067.

Step-by-step explanation:

Let the random variable X represent the amount of gas in Sarah's car.

It is provided that .

The amount of gas in a car is a continuous variable.

So, the random variable X follows a continuous uniform distribution.

Then the probability density function of X is:

For a continuous probability distribution the probability at an exact point is 0.

So, to compute the probability that the amount of gas in Sarah's car is exactly 7 gallons use continuity correction on both sides:

P (X = 7) = P (7 - 0.5 < X < 7 + 0.5)

              = P (6.5 < X < 7.5)

Thus, the probability that the amount of gas in Sarah's car is exactly 7 gallons is 0.067.

the dimensions are:

step-by-step explanation:

we want to find the dimensions of a rectangular box with volume of

we factor to obtain;

we rewrite the rightmost factor to obtain;

recall that:

we apply difference of two squares formula to obtain;

hence the dimensions are