Solve for x. 5(x – 10) = 30 – 15x x = 1 x = 4 x = 5 x = 8
2 answers:
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Answer:
The variance and standard deviation of <em>X</em> are 0.48 and 0.693 respectively.
The variance and standard deviation of (20 - <em>X</em>) are 0.48 and 0.693 respectively.
Step-by-step explanation:
The variable <em>X</em> is defined as, <em>X</em> = number of defective items in the sample.
In a sample of 20 items there are 4 defective items.
The probability of selecting a defective item is:
A random sample of <em>n</em> = 3 items are selected at random.
The random variable <em>X</em> follows a Binomial distribution with parameters <em>n</em> = 3 and <em>p </em>= 0.20.
The variance of a Binomial distribution is:
Compute the variance of <em>X</em> as follows:
Compute the standard deviation (σ (X)) as follows:
Thus, the variance and standard deviation of <em>X</em> are 0.48 and 0.693 respectively.
Now compute the variance of (20 - X) as follows:
Compute the standard deviation of (20 - X) as follows:
Thus, the variance and standard deviation of (20 - <em>X</em>) are 0.48 and 0.693 respectively.
Let's say you want to compute the probability 
where 
converges in distribution to 
, and follows a normal distribution. The normal approximation (without the continuity correction) basically involves choosing such that its mean and variance are the same as those for .
Example: If is binomially distributed with 
and 
, then has mean 
and variance 
. So you can approximate a probability in terms of with a probability in terms of :
where
follows the standard normal distribution.
Example: If
where