In a certain state, the daily amounts of industrial waste are normally distributed, with a mean of 5,000 tons and a standard deviation of 1,500 tons. Find the probability that on a randomly selected day the amount of industrial waste is greater than 6,695 tons. Use a table of the standard normal distribution to solve the problem. Round your answer to four decimal places.
A)0.1292
B)0.8708
C)0.5050
D)0.3609
E)0.3876

Question

In a certain state, the daily amounts of industrial waste are normally distributed, with a mean of 5,000 tons and a standard deviation of 1,500 tons. Find the probability that on a randomly selected day the amount of industrial waste is greater than 6,695 tons. Use a table of the standard normal distribution to solve the problem. Round your answer to four decimal places. ​
A)​0.1292
B)​0.8708
C)​0.5050
D)​0.3609
E)​0.3876

Quizplus · Accepted Answer

To find the probability that the amount of industrial waste is greater than 6,695 tons, we first convert the given value to a z-score using the formula $z = \frac{(X - \mu)}{\sigma}$, where $X$ is the value in question, $\mu$ is the mean, and $\sigma$ is the standard deviation. Substituting the given values, we get $z = \frac{(6695 - 5000)}{1500} = 1.13$. Looking up the z-score of 1.13 in the standard normal distribution table gives us the area to the left of the z-score, which is approximately 0.8708. Since we're interested in the probability of being greater than 6,695 tons, we subtract this value from 1, resulting in $1 - 0.8708 = 0.1292$.

In a Certain State, the Daily Amounts of Industrial Waste