Question

The newest model of smart car is supposed to get excellent gas mileage. A thorough study showed that gas mileage (measured in miles per gallon) is normally distributed with a mean of 75 miles per gallon and a standard deviation of 10 miles per gallon. What is the probability that, if driven normally, the car will get 100 miles per gallon or better? A. 1 - NORM.DIST(100, 75, 10, FALSE) B. NORM.DIST(100, 75, 10, FALSE) C. NORM.DIST(100, 75, 10, TRUE) D. 1 – NORM.DIST(100, 75, 10, TRUE)

Answer 1

Answer:

D. 1 – NORM.DIST(100, 75, 10, TRUE)

Step-by-step explanation:

Excel's Normal Distribution

The normal distribution has two parameters: the mean value $\mu$ and the standard deviation $\sigma$. Since it's a symmetric function the values at the right side of the center value

The normal distribution is a function which integral cannot be expressed in terms of elemental functions. That is why the cumulative probability is usually found in tables, graphs or any digital media like Excel.

The formula NORM.DIST computes the cumulative values for the left tail or $P( X < X_o)$ for a given mean and standard deviation. The parameters are

$NORM.DIST (X_o,\mu,\sigma,cumulative)$

This last parameter tells the formula we want the cumulative left-tail probability or just the value at Xo. This value must be set to TRUE to compute the probability for a range of values, like in the problem at hand.

Since the formula computes the left-tail of the function, we must take advantage of the symmetry of the distribution if we want to compute right-tail values we just subtract the result from 1.

Thus, the correct formula to calculate the required probability is

D. 1 – NORM.DIST(100, 75, 10, TRUE)