The Professor's Response

If a person bought 1 share of Google stock within the last year, what is the probability that the stock on that day closed within $50 of the mean for that year (round to two places)? (Hint: this means the probability of being between 50 below and 50 above the mean). I cannot figure out the formula for this.. please help:)

M=1131.530876

SD=64.81327423

See the professor's answer below.

Is there any assumption about the distribution of the stock price? Does it say we can assume the share price is normally distributed with a mean of $1,131.53 and a standard deviation of $64.81? If so, you can calculate the z score for the two limits of the region bounded by +/- $50 from the mean.

In other words, the lower bound of the region is (the mean - $50) $1,081.53 and the upper bound is (the mean + 50) $1,181.53. Then the corresponding z scores are:

z = (1081.53 - 1131.53)/64.81 = -50/64.81327423 = -0.77. The other z score is 0.77. Then using the standard normal table, we can look up 0.77 to determine the area between 0 and 0.77, which gives us: 0.2794. The area from -0.77 to 0 is also 0.2794, so the total area is 0.5588 or 55.88%. However, this is only true if the share prices follow a normal distribution.