Question

A soft drink machine outputs a mean of 26 ounces per cup. The machine's output is normally distributed with a standard deviation of 3 ounces. What is the probability of filling a cup between 22 and 31 ounces? Round your answer to four decimal places.

Answer 1

The probability of filling a cup between 22 and 31 ounces is 0.8607, rounded to four decimal places.

Step-by-step explanation:

To find the probability of filling a cup between 22 and 31 ounces, we need to calculate the z-scores for these values and then use the standard normal distribution table.

The z-score formula is: z = (x - μ) / σ, where x is the value, μ is the mean, and σ is the standard deviation.

For 22 ounces: z = (22 - 26) / 3

= -4/3

= -1.33

For 31 ounces: z = (31 - 26) / 3 = 5/3

= 1.67

Using the standard normal distribution table (or calculator), we can find the probabilities corresponding to these z-scores:

Probability for z = -1.33: 0.0918

Probability for z = 1.67: 0.9525

To find the probability of filling a cup between 22 and 31 ounces, we subtract the probability for 22 ounces from the probability for 31 ounces:

0.9525 - 0.0918 = 0.8607

Therefore, the probability of filling a cup between 22 and 31 ounces is 0.8607 (rounded to four decimal places).