A bakery owner wants to ensure they make enough cookies each day to meet the demand from customers. On average, they sell 92 cookies a day with a standard deviation of 9. The baker makes 70 cookies each day. Using a calculator or a spreadsheet program, find the probability that the baker made enough cookies (no more than 70 cookies sold that day). Round the answer to the nearest tenth of a percent.

1 answer

To find the probability of selling no more than 70 cookies when the average is 92 with a standard deviation of 9, we can use the z-score formula:

z = (X - μ) / σ

Where:
X = 70 (number of cookies made)
μ = 92 (average number of cookies sold)
σ = 9 (standard deviation)

Calculating the z-score:
z = (70 - 92) / 9
z = -22 / 9
z = -2.44

Next, we need to find the probability associated with this z-score using a standard normal distribution table or calculator. The probability of selling no more than 70 cookies is the area to the left of the z-score of -2.44.

Looking up -2.44 in a standard normal distribution table or using a calculator, we find the probability to be approximately 0.0073.

Therefore, the probability that the baker made enough cookies (no more than 70 cookies sold that day) is approximately 0.73%.