Answer:
And 
and if we use the following function on the Ti84 plus we got:
invNorm(0.02,0,1)
invNorm(1-0.02,0,1)
And the values with the middle 96% of the values are:
Step-by-step explanation:
For this case we want to find the limits with the middle 96% of the area below the normal curve, then the significance level would be:
And and if we use the following function on the Ti84 plus we got:
invNorm(0.02,0,1)
invNorm(1-0.02,0,1)
And the values with the middle 96% of the values are:
Answer:
Step-by-step explanation:
Given
--- slots
i.e. even numbers between 1 and 34 (inclusive)
Required
The probabiity of winning is the number of even numbers divided by the total slot;
i.e.
So, we have:
Base case: if <em>n</em> = 1, then
1² - 1 = 0
which is even.
Induction hypothesis: assume the statement is true for <em>n</em> = <em>k</em>, namely that <em>k</em> ² - <em>k</em> is even. This means that <em>k</em> ² - <em>k</em> = 2<em>m</em> for some integer <em>m</em>.
Induction step: show that the assumption implies (<em>k</em> + 1)² - (<em>k</em> + 1) is also even. We have
(<em>k</em> + 1)² - (<em>k</em> + 1) = <em>k</em> ² + 2<em>k</em> + 1 - <em>k</em> - 1
… = (<em>k</em> ² - <em>k</em>) + 2<em>k</em>
… = 2<em>m</em> + 2<em>k</em>
… = 2 (<em>m</em> + <em>k</em>)
which is clearly even. QED
