We have been given that the lifespans of lions in a particular zoo are normally distributed. The average lion lives 12.5 years; the standard deviation is 2.4 years. We are asked to find the probability of a lion living longer than 10.1 years using empirical rule.
First of all, we will find the z-score corresponding to sample score 10.1.
, where,
z = z-score,
x = Random sample score,
= Mean
= Standard deviation.
![z=\frac{10.1-12.5}{2.4}](https://tex.z-dn.net/?f=z%3D%5Cfrac%7B10.1-12.5%7D%7B2.4%7D)
![z=\frac{-2.4}{2.4}](https://tex.z-dn.net/?f=z%3D%5Cfrac%7B-2.4%7D%7B2.4%7D)
![z=-1](https://tex.z-dn.net/?f=z%3D-1)
Since z-score of 10.1 is
. Now we need to find area under curve that is below one standard deviation from mean.
We know that approximately 68% of data points lie between one standard deviation from mean.
We also know that 50% of data points are above mean and 50% of data points are below mean.
To find the probability of a data point with z-score
, we will subtract half of 68% from 50%.
![\frac{68\%}{2}=34\%](https://tex.z-dn.net/?f=%5Cfrac%7B68%5C%25%7D%7B2%7D%3D34%5C%25)
![50\%-34\%=16\%](https://tex.z-dn.net/?f=50%5C%25-34%5C%25%3D16%5C%25)
Therefore, the probability of a lion living longer than 10.1 years is approximately 16%.
Answer:
![\huge\boxed{n=8}](https://tex.z-dn.net/?f=%5Chuge%5Cboxed%7Bn%3D8%7D)
Step-by-step explanation:
![-\dfrac{3}{4}n=-6\qquad|\text{multiply both sides by (-4)}\\\\(-4\!\!\!\!\diagup)\left(-\dfrac{3}{4\!\!\!\!\diagup}n\right)=(-4)(-6)\\\\3n=24\qquad|\text{divide both sides by 3}\\\\\dfrac{3\!\!\!\!\diagup n}{3\!\!\!\!\diagup}=\dfrac{24\!\!\!\!\!\diagup}{3\!\!\!\!\diagup}\\\\n=8](https://tex.z-dn.net/?f=-%5Cdfrac%7B3%7D%7B4%7Dn%3D-6%5Cqquad%7C%5Ctext%7Bmultiply%20both%20sides%20by%20%28-4%29%7D%5C%5C%5C%5C%28-4%5C%21%5C%21%5C%21%5C%21%5Cdiagup%29%5Cleft%28-%5Cdfrac%7B3%7D%7B4%5C%21%5C%21%5C%21%5C%21%5Cdiagup%7Dn%5Cright%29%3D%28-4%29%28-6%29%5C%5C%5C%5C3n%3D24%5Cqquad%7C%5Ctext%7Bdivide%20both%20sides%20by%203%7D%5C%5C%5C%5C%5Cdfrac%7B3%5C%21%5C%21%5C%21%5C%21%5Cdiagup%20n%7D%7B3%5C%21%5C%21%5C%21%5C%21%5Cdiagup%7D%3D%5Cdfrac%7B24%5C%21%5C%21%5C%21%5C%21%5C%21%5Cdiagup%7D%7B3%5C%21%5C%21%5C%21%5C%21%5Cdiagup%7D%5C%5C%5C%5Cn%3D8)
A driver can be jailed up to one year and fined up to $5,000 if he or she refuses to bring his or her vehicle to a stop when given a visual or an audible signal by a police officer.
Answer: Option B
<u>Step-by-step explanation:</u>
This Vehicle codes 2800.1 state a violation or avoidance of police. The rules as follows: "Any person who, while driving a motor vehicle and intentionally avoiding it, intentionally escapes or attempts to escape from a peace officer " Any driver who "intentionally fails or refuses to stop the vehicle or otherwise, an attempt to escape or prosecute the pursuing police officer when he receives a visual and audible signal to stop the vehicle.
"Visual and audible" signals include sirens, lights, hand signals and voice commands. You must have been able to hear and / or see these signals to be accused of escaping and attempting to escape from the police. This is a level II or level 3 crime, and any penalties for those fleeing or trying to avoid a police officer will depend on the scale of the crime they are suspected of.
- Second-Degree Misdemeanour - in jail maximum of 2 years and fine max. of $5,000
- Third-Degree Felony - in jail maximum of 7 years and fine max. of $15,000.
Answer:
<h2>
y = - 2x</h2>
Step-by-step explanation:
An equation in point-slope form of the line passing through point <em>P(x₁, y₁)</em> with slope <em>m</em>: y - y₁ = m(x - x₁)
m = -2
P(-3, 6) ⇒ x₁ = -3, y₁ = 6
y - 6 = -2(x - (-3))
y - 6 = -2(x + 3) ← point-slope form
y - 6 = -2x - 6 {add 6 to both sides}
y = - 2x ← slope-intercept form {intercept=0}
Answer:
A. This is a linear function because there is a common difference of 2
Step-by-step explanation:
Differences are ...
The differences of 2 are common, so this is an arithmetic function.