1. Since we know that our data is normally distributed, this means that the mean is exactly at the center of the data we are going to look at. Since we know that this is the case this means that the mean must have 50% of the data below it and 50% of the data above, so we can say that the probability that the stock closes at less than the mean is 50% (probability that the value is to the left of the mean on the normal graph).

2. The first thing that we have to do is calculate the mean and standard deviation of the close prices in the excel spreadsheet (done on attached file). Now we want to use the formula z = x-mean/sd = 400-550.5/23.8 = -6.32 which is our z value. Now we want to use the table to find the probability that we get a value greater than 400 so we want to solve 1- the probability corresponding to z=-6.32 in the table =1-0 = 100% (this is expected because if you look at the close values they are all up around the 500s so 400 would be very very unexpected). …show more content…
Here we want to use the same formula but solve it for 45 in each direction so we solve (505.5-550.5)/23.8 = -1.89 and (595.5-550.5)/23.8 = 1.89. Now we look at the z table and see that we get probabilities of 0.0294 and 0.9706 respectively. Since we want the probability within that range we take the upper range minus the lower to give us the middle range so we solve 0.9706-0.0294 =