Data set is normally distributed with a mean of 27 and a standard deviation of 3.5. Find the Z-score for a value of 25, to the n
2 answers:
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Answer:
6 and 2/3
Step-by-step explanation:
24 + 8 + 6/14 + 1/14 =
32 + 7/14 =
32 1/2
Answer:
<h2>Answer:
a)0.62% probability that total sick leave for next month will be less than 150 hours.
b) 225.6 hours should be budgeted for sick leave if that amount is to be exceeded with a probability of only 0.10.
Step-by-step explanation:
Problems of normally distributed samples can be solved using the z-score formula.
In a set with mean and standard deviation
, the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.
In this problem, we have that:
a.Find the probability that total sick leave for next month will be less than 150 hours.
This probability is the pvalue of Z when X = 150. So:
has a pvalue of 0.0062.
So there is a 0.62% probability that total sick leave for next month will be less than 150 hours.
b.In planning schedules for next month, how much time should be budgeted for sick leave if that amount is to be exceeded with a probability of only 0.10.
This is the value of X when Z has a pvalue of 0.90. So
225.6 hours should be budgeted for sick leave if that amount is to be exceeded with a probability of only 0.10.
We have a number line as indicated in the figure above. From this figure we know that the <em>x-values</em> <em>increase f</em><em>rom left to right</em>. So we need to write the solution<span> that matches the previous graph. Taking a look on the graph we see that 
begins in -3 and closes in 8, that is, <em>takes values from -3 to 8</em>. In a mathematical language this is given by the following statement:
</span>![x \in [-3,8]](https://tex.z-dn.net/?f=x%20%5Cin%20%5B-3%2C8%5D)
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