Question

Problem 2: Note: For EACH of the following part, draw a normal curve, mark the x-axis accordingly. and highlight the corresponding areas. Round z-scores to the SECOND decimal place, and keep the ORIGINAL FOUR decimal places for the probability. The average number of miles driven on a full tank of gas in a Hyundai Veracruz before its low-fuel light comes on is 320. Assuming this mileage follows the normal distribution with a standard deviation of 20 miles. What is the probability that, before the low-fuel light comes on, the car will travel

WHAT IS THE SCORE IN THE LOWER QUARTILE (Q1)?

*****Hints: you should recognize "lower quartile (Q1)" as the Lower 25% (LEFT tail area) under the normal curve, then find the z-score, and calculate the "x" using the z-score formula.

Answer 1

The lower quartile is the lower 25% under the normal curve. From the standard normal table, z-score for 25% percentile is -0.6745

Then, x = $\mu$ + z $\sigma$

=> x = 320 - 0.6745 * 20 = 306.51 miles