In a certain state, the daily amounts of industrial waste are normally distributed, with a mean of 9,000 tons and a standard deviation of 1,000 tons. Find the probability that on a randomly selected day the amount of industrial waste is less than 7,000 tons. Use a table of the standard normal distribution to solve the problem. Round your answer to four decimal places.
A)0.9772
B)0.1836
C)0.7936
D)0.0228
E)0.7720

Question

In a certain state, the daily amounts of industrial waste are normally distributed, with a mean of 9,000 tons and a standard deviation of 1,000 tons. Find the probability that on a randomly selected day the amount of industrial waste is less than 7,000 tons. Use a table of the standard normal distribution to solve the problem. Round your answer to four decimal places. ​
A)0.9772
B)0.1836
C)0.7936
D)0.0228
E)0.7720

Quizplus · Accepted Answer

To solve the problem, we need to standardize the value of 7,000 tons using the formula z = (x-μ)/σ where x is the value we want to standardize (7,000), μ is the mean (9,000), and σ is the standard deviation (1,000). Substituting the given values, we get:

z = (7,000 - 9,000)/1,000 = -2

Next, we need to find the probability that a standard normal random variable is less than -2. Using a table of the standard normal distribution, we look for the row corresponding to -2 and the column corresponding to the second decimal place, which gives us 0.0228. This means that the probability of getting a standardized value less than -2 is 0.0228, or approximately 2.28%. Therefore, the probability of getting a daily amount of industrial waste less than 7,000 tons is also 0.0228 or 2.28%.

In a Certain State, the Daily Amounts of Industrial Waste