10) The amount spent per month by employees for parking at a municipal lot is normally distributed with a mean of $60 and a standard deviation of $5. a) About what percentage of the observations lie between $55 and $65? b) About what percentage of the observations lie between $50 and $70? a) About what percentage of the observations lie between $45 and $75?
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Ответ:
a)![P(55](/tpl/images/0591/2988/f5f0e.png)
And we can find this probability with this difference:
And in order to find these probabilities we can using tables for the normal standard distribution, excel or a calculator.
And that represent 68.2%
b)![P(50](/tpl/images/0591/2988/1b26d.png)
And we can find this probability with this difference:
And in order to find these probabilities we can using tables for the normal standard distribution, excel or a calculator.
And that represent 95.42%
c)![P(45](/tpl/images/0591/2988/f988a.png)
And we can find this probability with this difference:
And in order to find these probabilities we can using tables for the normal standard distribution, excel or a calculator.
And that represent 97.73%
Explanation:
Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
Part a
Let X the random variable that represent the amount spent per month by employees of a population, and for this case we know the distribution for X is given by:
Where
and ![\sigma=5](/tpl/images/0591/2988/f59b4.png)
We are interested on this probability
And the best way to solve this problem is using the normal standard distribution and the z score given by:
If we apply this formula to our probability we got this:
And we can find this probability with this difference:
And in order to find these probabilities we can using tables for the normal standard distribution, excel or a calculator.
And that represent 68.2%
Part b
And we can find this probability with this difference:
And in order to find these probabilities we can using tables for the normal standard distribution, excel or a calculator.
And that represent 95.42%
Part c
And we can find this probability with this difference:
And in order to find these probabilities we can using tables for the normal standard distribution, excel or a calculator.
And that represent 97.73%
Ответ: