Question

A gasoline tank for a certain car is designed to hold 19 gallons of gas. Suppose that the random variable actual capacity of a randomly selected tank has a distribution that is well approximated by a normal curve with mean 19.0 gallons and standard deviation 0.2 gallon.

What is the probability that a randomly selected tank will hold at least 18.9 gallons?

Answer 1

To find the probability that a randomly selected tank will hold at least 18.9 gallons, we need to find the area under the normal curve to the right of 18.9. Using the formula z = (x - mean) / standard deviation, the z-score for 18.9 is -0.5. Looking up the area to the right of -0.5 in the standard normal distribution table, we find that the probability is approximately 0.6915.

Step-by-step explanation:

To find the probability that a randomly selected tank will hold at least 18.9 gallons, we need to find the area under the normal curve to the right of 18.9. Since the random variable follows a normal distribution with mean 19.0 and standard deviation 0.2, we can convert the value 18.9 into a z-score and then find the area using a standard normal distribution table or calculator.

Using the formula z = (x - mean) / standard deviation, the z-score for 18.9 is:

z = (18.9 - 19.0) / 0.2 = -0.5

Looking up the area to the right of -0.5 in the standard normal distribution table, we find that the probability is approximately 0.6915. Therefore, the probability that a randomly selected tank will hold at least 18.9 gallons is 0.6915 or 69.15%.