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ginocousins06
03.12.2019 •
Mathematics
The average gre score at the university of pennsylvania for the incoming class of 2016-2017 was 311. assume that the standard deviation was 13.
if you select a random sample of 40 students, what is the probability that the sample mean will be greater than 308? round your answer to three decimal places.
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Ответ:
Step-by-step explanation:
1) 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".
Let X the random variable that represent the GRE score at the University of Pennsylvania for the incoming class of 2016-2017, and for this case we know the distribution for X is given by:
And let
represent the sample mean, the distribution for the sample mean is given by:
On this case![\bar X \sim N(311,\frac{13}{\sqrt{40}})](/tpl/images/0400/2527/52a44.png)
2) Calculate the probability
We want this probability:
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:
Ответ:
4 categories are shown in rows.
2 categories are shown in columns.
12 14 year olds.
82 people were polled.