Half the difference of a number and 18 is equivalent to -25. find the number
1 answer:
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Answer:
0.6826 = 68.26% probability Z will be within one standard deviation of average.
Step-by-step explanation:
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean and standard deviation
, the z-score of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
What is the probability Z will be within one standard deviation of average?
This is the p-value of Z = 1 subtracted by the p-value of Z = -1.
Z = 1 has a p-value of 0.8413.
Z = -1 has a p-value of 0.1587.
0.8413 - 0.1587 = 0.6826
0.6826 = 68.26% probability Z will be within one standard deviation of average.
From the pool of 5 letters, we're picking 4. We can arrange the 4 we picked in 
ways.
But there are 5 ways of *not* picking the remaining letter. To account for the arrangements containing the letter not picked, we multiply this total by 5.
Put another way, suppose we drew a, b, c, and d, but not e. We have 24 possible arrangements for these 4 letters, but for any distinct arrangement there are 5 ways of replacing any letter with e.
So the number of arrangements we can actually make is
.
But there are 5 ways of *not* picking the remaining letter. To account for the arrangements containing the letter not picked, we multiply this total by 5.
Put another way, suppose we drew a, b, c, and d, but not e. We have 24 possible arrangements for these 4 letters, but for any distinct arrangement there are 5 ways of replacing any letter with e.
So the number of arrangements we can actually make is