Solution
The z-score, also referred to as standard score, z-value, and normal score, among other things, is a dimensionless quantity that is used to indicate the signed, fractional, number of standard deviations by which an event is above the mean value being measured. Values above the mean have positive z-scores, while values below the mean have negative z-scores.
Mean is $650
Standard deviation = $50
Therefore the estimated percent of apartment residents = 81.86%
Answer:
1)
2)
Other conditions that are important are:
3) n is large
4) p is close to 1/2 or 0.5
Step-by-step explanation:
1) Previous concepts
The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".
2) Solution to the problem
Let X the random variable of interest, on this case we now that:
The probability mass function for the Binomial distribution is given as:
Where (nCx) means combinatory and it's given by this formula:
In order to apply the normal apprximation we need to satisfy these two conditions:
1)
2)
Other conditions that are important are:
3) n is large
4) p is close to 1/2 or 0.5
