The ellipse with center C(2, -3), vertices V(-8,-3) and V2(12,-3), and foci F1(-4,-3) and F2(8,-3). 6.
1 answer:
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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.
Answer:
Option B.
Step-by-step explanation:
The given vertices of triangle ABC are (-1, -1), (-1, -5) and (0.5, -5).
We need to find the coordinates of triangle when it is translated two units left.
So, the rule of translation is
Using this rule, we get
The vertices of triangle A'B'C' are A'(-3,-1), B'(-3,-5) and C'(-1.5,-5).
Therefore, the correct option is B.