Answer:
Step-by-step explanation:
We can use basic probability to find the probability that this roll is not a factor of 35.
First off, we know that with a six sided die there are 6 possible things we can roll.
1, 2, 3, 4, 5, or 6
Now, what are the factors of 35? The factors of 35 will be any whole number that can be multiplied by another whole number to get 35.
- We know
, so two factors are 1 and 35. - We know
, so two factors are 5 and 7.
Therefore, the factors of 35 are 1, 5, 7, 35.
Both 5 and 7 are inside the range of 1-6. So the probability of rolling a side that's a factor of 35 will be 
since there are two factors and 6 possible options.
This means, logically, there is a 
chance of not rolling a factor of 35.
Hope this helped!
The mode would be 17, it’s the number that appears the most. I’m not rewriting it though
Transform <em>Y</em> to <em>Z</em>, which is distributed N(0, 1), using the formula
<em>Y</em> = <em>µ</em> + <em>σZ</em>
where <em>µ</em> = -16 and <em>σ</em> = 1.21.
Pr[-15.043 < <em>Y</em> ≤ <em>k</em>] = 0.1546
Pr[(-15.043 + 16)/1.21 < (<em>Y</em> + 16)/1.21 ≤ (<em>k</em> + 16)/1.21] = 0.1546
Pr[0.791 < <em>Z</em> ≤ (<em>k</em> + 16)/1.21] ≈ 0.1546
Pr[<em>Z</em> ≤ (<em>k</em> + 16)/1.21] - Pr[<em>Z</em> < 0.791] = 0.1546
Pr[<em>Z</em> ≤ (<em>k</em> + 16)/1.21] = 0.1546 + Pr[<em>Z</em> < 0.791]
Pr[<em>Z</em> ≤ (<em>k</em> + 16)/1.21] ≈ 0.1546 + 0.786
Pr[<em>Z</em> ≤ (<em>k</em> + 16)/1.21] ≈ 0.940
Take the inverse CDF of both sides (<em>Φ(x)</em> denotes the CDF itself):
(<em>k</em> + 16)/1.21 ≈ <em>Φ⁻¹</em> (0.940) ≈ 1.556
Solve for <em>k</em> :
<em>k</em> + 16 = 1.21 • 1.556
<em>k</em> ≈ -14.118
