Answer
a)mean=2.5, standard deviation=1.44.
b) yes.
Work Step by Step
a) By using the given formula and data:$mean=\frac{max+min}{2}=\frac{5+0}{2}=2.5.$
range=maximum-minimum=5-0=5.
standerd deviation=$\frac{range}{\sqrt {12}}=\frac{5}{\sqrt {12}}=1.44.$
b)If the standard deviation is 1, then by the given formula we know that the range is $\sqrt {12}$
Then the probability is the range of the given interval divided by the range of the distribution:P(x is between -1 and 1):$\frac{1-(-1)}{\sqrt {12}}=0.5774$
Using the table, the probability of z being between -1 and 1 is equal to the probability of z being less than 1 minus the probability of z being less than -1, which is: 0.8413-0.1587=0.6826
The difference between the results is more than 0.1, which is quite big, hence the answer is yes.
