Question

The mean cost of gas in the U.S (in November, 2022) is $3.74 per gallon with a standard deviation of \$0.21. Gas prices in the U.S. are know are known to normally distributed. a) Find and interpret the z-score for a gas price of $2.97 per gallon. b) If you randomly selected a gas station in the U.S. (in November, 2022), what is the probability that the gas at that station costs less than $3.53

Answer 1

a) The z-score for a gas price of $2.97 per gallon is approximately -3.67, indicating it is about 3.67 standard deviations below the mean. b) The probability that the gas at a randomly selected gas station costs less than $3.53 is approximately 0.1587, or 15.87%.

Step-by-step explanation:

a) To find the z-score for a gas price of $2.97 per gallon, we can use the formula: z = (x - mean) / standard deviation. Plugging in the values, we get: z = (2.97 - 3.74) / 0.21 ≈ -3.67. The z-score represents the number of standard deviations the data point is away from the mean. In this case, the gas price of $2.97 per gallon is approximately 3.67 standard deviations below the mean.

b) To find the probability that the gas at a randomly selected gas station costs less than $3.53, we need to find the area under the normal distribution curve to the left of $3.53. We can use the z-score formula to standardize the value: z = (x - mean) / standard deviation. Plugging in the values, we get: z = (3.53 - 3.74) / 0.21 ≈ -1. Using a standard normal distribution table or a calculator, we can find that the probability is approximately 0.1587, or 15.87%.