Question

The miles-per-gallon rating of passenger cars is a normally distributed random variable with a mean of 33.8 mpg and a standard deviation of 3.5 mpg. a) What is the probability that a randomly selected passenger car gets more than 37.3 mpg

Answer 1

Answer:

The probability that a randomly selected passenger car gets more than 37.3 mpg is 0.1587.

Step-by-step explanation:

Let the random variable X represent the miles-per-gallon rating of passenger cars.

It is provided that $X\sim N(\mu=33.8,\ \sigma^{2}=3.5^{2})$.

Compute the probability that a randomly selected passenger car gets more than 37.3 mpg as follows:

$P(X>37.3)=P(\frac{X-\mu}{\sigma}>\frac{37.3-33.8}{3.5})$

                   $=P(Z>1)\\\\=1-P(Z$

Thus, the probability that a randomly selected passenger car gets more than 37.3 mpg is 0.1587.