Do you remember the problem highlighting students tardy to Ms. Greene’s class? Now that you have investigated how to create and use a normal distribution, model the number of tardy students Ms. Greene actually recorded using a normal distribution. The data Ms. Greene gathered for $30$ days is shown in the table below.

1. On your calculator, recreate the relative frequency histogram for the number of tardy students per day that is shown in problem 4-76.

   Answer (a):

   

2. What are the mean and standard deviation of the number of tardy students per day?

3. On your calculator, model the data with a normal distribution by pressing $\boxed{\text{Y=}}$ and entering $\boxed{\text{2nd}}$ [DISTR] normalpdf($X$, mean, standard deviation). Sketch the model with the histogram.

4. According to your model, on what percentage of days were four or more people tardy? Shade this proportion on a new sketch of the model, and calculate the proportion using normalcdf(lower, upper, mean, standard deviation) on your calculator.

   Answer (d):

   $\approx13.4\%$
   Be sure to sketch and shade the model.

5. Assume that the last $30$ days in Ms. Greene’s class were representative of the $180$ days in the whole school year. According to your model, how many days this year can Ms. Greene expect four or more tardy students?

   Hint (e):

   normalcdf$(4, 10\text{^}99, 2.7333, 1.1427)$