Of police academy applicants, only 25% will pass all the examinations. suppose that 12 successful candidates are needed. what is
1 answer:
The probability is 0.0008.
I used a binomial probability on this one, since there are two outcomes (either pass or fail); the events are independent (the probability of one person passing does not influence the probability of another passing); and there are a fixed number of trials (in this case, 20).
For binomial probabilities, we use the formula:
With our information, we have:
I used a binomial probability on this one, since there are two outcomes (either pass or fail); the events are independent (the probability of one person passing does not influence the probability of another passing); and there are a fixed number of trials (in this case, 20).
For binomial probabilities, we use the formula:
With our information, we have:
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Answer:
The sample size required is 2500.
Step-by-step explanation:
z-score:
In function of the margin of error M, the z-score is given by:
In this question, we have that:
So
The sample size required is 2500.
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