Answer:
C. The population must be normally distributed.
Step-by-step explanation:
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean 
and standard deviation 
, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean and standard deviation 
.
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For us to apply the central limit theorem with a sample size of 14, the underlying population must be normally distributed.
So the correct answer is:
C. The population must be normally distributed.
A tree diagram can be drawn for a clearer understanding. The branches of the tails can be ignored since we are not concerned about that. To find the probability along the branches, we just have to multiply the probabilities of each branch, giving you an answer of 1/128
Answer:
Step-by-step explanation:
-3x^4 -9x^3+ 15x^2
-3x^2 ( x^2 + 3x -5)
if you use quadratic formula (see image)
~~~~~~~~~~~~~~~~~~~~~~
10x^3 -35x^2 +6x -21
5x2(2x-7) +3(2x-7)
(5
+ 3) (2x-7)
Since the dice are fair and the rolling are independent, each single outcome has probability 1/15. Every time we choose
We have 
and 
, because the dice are fair.
Now we use the assumption of independence to claim that
Now, we simply have to count in how many ways we can obtain every possible outcome for the sum. Consider the attached table: we can see that we can obtain:
- 2 in a unique way (1+1)
- 3 in two possible ways (1+2, 2+1)
- 4 in three possible ways
- 5 in three possible ways
- 6 in three possible ways
- 7 in two possible ways
- 8 in a unique way
This implies that the probabilities of the outcomes of 
are the number of possible ways divided by 15: we can obtain 2 and 8 with probability 1/15, 3 and 7 with probability 2/15, and 4, 5 and 6 with probabilities 3/15=1/5
Answer:
Step-by-step explanation:
Given 2 similar figures with ratio of sides = a : b, then
ratio of areas = a² : b²
Here ratio of sides = 52 : 68 = 13 : 17 ← in simplest form, thus
ratio of areas = 13² : 17² = 169 : 289 =
