The distance formula is , where
and
are the points.
Substitute in the points.
Subtract.
Solve the exponents.
Add.
Now, we can simplify this square root just a little bit. has a square factor of
.
The square root of equals
.
Select other ways to express 10^{4}
2 answers:
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Answer:
(a) The distribution of is a Binomial distribution.
(b) The sampling distribution of the sample mean will be approximately normal.
(c) The value of is 0.50.
Step-by-step explanation:
It is provided that random variables are independent and identically distributed Bernoulli random variables with <em>p</em> = 0.50.
The random sample selected is of size, <em>n</em> = 100.
(a)
Theorem:
Let be independent Bernoulli random variables, each with parameter <em>p</em>, then the sum of of thee random variables,
is a Binomial random variable with parameter <em>n</em> and <em>p</em>.
Thus, the distribution of is a Binomial distribution.
(b)
According to the Central Limit Theorem if we have an unknown population with mean <em>μ</em> and standard deviation <em>σ</em> and appropriately huge random samples (<em>n</em> > 30) are selected from the population with replacement, then the distribution of the sample mean will be approximately normally distributed.
The sample size is large, i.e. <em>n</em> = 100 > 30.
So, the sampling distribution of the sample mean will be approximately normal.
The mean of the distribution of sample mean is given by,
And the standard deviation of the distribution of sample mean is given by,
(c)
Compute the value of as follows:
*Use a <em>z</em>-table.
Thus, the value of is 0.50.
Given:
A spinner marked A, B, C is spun then a 6-sided die is rolled.
To find:
The probability of getting a B and then a 6.
Solution:
We know that,
Total possible values for a spinner are 3. So, the probability of getting B, we get
Total possible values for a die are 6. So, the probability of getting 6, we get
Now, the probability of getting a B and then a 6 is
The required probability is .
Therefore, the correct option is D.