The list below gives the number of patrons per day over a 30-day period
during July at a theatre.
127 126 125 132 128 122 156 172
183 171 160 140 154 160 122 187
185 158 112 145 168 187 117 120
171 171 156 163 168 162
a) Find the mean and standard deviation of these data.
b) Determine the probability that a day selected randomly from this sample
had at least 160 patrons. State and justify any assumptions you have
made.
So I got 151.6 for the mean and 23.31 for the standard deviation. However for Part B, I got 0.3594 instead of 0.3673.
To get my answer, I did 160-151.6/23.31 = 0.36.
Then I looked up 0.36 on the normal distribution table and got 0.6406.
Then, 1-0.6406=0.3594.
Why is my answer wrong?
The population standard deviation is 22.92.
You would use that here because the question refers only to what is happening within this set of data, so it becomes the population rather than the sample.
However, that still doesn't deliver the correct answer according to your post.
Perhaps a piece of data has been copied down incorrectly?