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From the given data sets we shall obtain the answers as follows:
<span>301 345 305 394 328 317 361 325 310 362
Re-arrange the data in ascending order:
301, 305, 310, 317,325, 328, 345, 361, 362, 394
from the above we see that:
Minimum value=301
Q1=310
median=(325+328)/2=326.5
Q3=361
Maximum value=394
Thus the box plot will be as follows:
</span>
<span>301 345 305 394 328 317 361 325 310 362
Re-arrange the data in ascending order:
301, 305, 310, 317,325, 328, 345, 361, 362, 394
from the above we see that:
Minimum value=301
Q1=310
median=(325+328)/2=326.5
Q3=361
Maximum value=394
Thus the box plot will be as follows:
</span>
Answer:
If we divide both sides by we got:
And we can use the normal distribution table or excel to find the probabilites and we got:
Step-by-step 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".
Solution to the problem
Let X the random variable that represent the area of a population, and for this case we know the distribution for X is given by:
Where and
We select a a sample of n =4 and since the distribution for X is normal then we know that the distribution for the sample mean is given by:
And we want to find this probability:
If we divide both sides by we got:
And we can use the normal distribution table or excel to find the probabilites and we got: