Question

The mass of tea in "Supacuppa" teabags follows a normal distribution with a mean of 4.1 g and a standard deviation of 0.12 g. Find the probability that a randomly chosen Supacuppa teabag contains more than 4.0 g of tea.

Answer 1

To find the probability that a randomly chosen Supacuppa teabag contains more than 4.0 g of tea, we can use the standard normal distribution. The probability is approximately 0.7967, or 79.67%.

Step-by-step explanation:

To find the probability that a randomly chosen Supacuppa teabag contains more than 4.0 g of tea, we can use the standard normal distribution.

First, we need to standardize the value of 4.0 g using the formula:

Z = (X - mean) / standard deviation. Plugging in the values, we get: Z = (4.0 - 4.1) / 0.12 = -0.83.

We can then use a standard normal distribution table to find the probability associated with a Z-score of -0.83, which is approximately 0.2033.

However, since we want the probability of a teabag containing more than 4.0 g of tea, we need to subtract this probability from 1.

So, the final probability is approximately 1 - 0.2033 = 0.7967, or 79.67%.