Commuters were asked how many times a week they stop for coffee on their way to work. A survey found a mean of 3 times a week with a standard deviation of 0.55. What is the probability that in a group of 36 people they stop between 2.8 and 3.25 times per week?

To find the probability that in a group of 36 people they stop between 2.8 and 3.25 times per week, we can use the z-score and the standard normal distribution.

First, let's calculate the z-scores for both values:

z1 = (2.8 - 3) / 0.55
z2 = (3.25 - 3) / 0.55

Using these z-scores, we can now look up the corresponding area under the standard normal distribution curve using a z-table or a statistical calculator.

The area under the curve between the two z-scores represents the probability that a random individual from this group will stop between 2.8 and 3.25 times per week.

P(2.8 < X < 3.25) = P(z1 < Z < z2)

Once you have the z-scores, you can look up the corresponding probabilities from a standard normal distribution table or use a statistical calculator. The probabilities will be between 0 and 1.

Note: Make sure to use the cumulative probability when looking up values in the table or calculator.

You can also use a calculator such as Excel or Python to calculate the probability directly using the formula for the standard normal distribution. The formula is:

P(x) = (1 / sqrt(2 * pi)) * integral(e^(-t^2 / 2), -inf, x)

Where x represents the z-score and the integral represents the area under the curve from negative infinity (-inf) to x.

By using these methods, you can find the probability that in a group of 36 people, they stop between 2.8 and 3.25 times per week.