Suppose the thickness of the blacktop on a road that has recently been resurfaced is normal with a mean of 6 cm and a standard deviation of 0.4 cm. What percentage of the blacktop is at least 5 cm thick?
A) 0.883
B) 0.994
C) 0.006
D) 0.722
E) 0.432

Question

Quizplus · Accepted Answer

To find the percentage of the blacktop that is at least 5 cm thick, we calculate the Z-score for 5 cm and then find the corresponding cumulative probability. The Z-score is calculated as $Z = \frac{X - \mu}{\sigma}$, where $X$ is the value of interest (5 cm), $\mu$ is the mean (6 cm), and $\sigma$ is the standard deviation (0.4 cm). Plugging in the values, we get $Z = \frac{5 - 6}{0.4} = -2.5$. Looking up the Z-score of -2.5 in a standard normal distribution table or using a calculator, we find that the cumulative probability to the left of Z = -2.5 is approximately 0.0062. Since we are interested in the percentage of the blacktop that is at least 5 cm thick, we subtract this value from 1 (since 1 represents the whole distribution) to get 0.9938 or 99.38%, which is approximately 99.4% when rounded to three decimal places. This corresponds to choice B.

Suppose the Thickness of the Blacktop on a Road That