Ying Zyiyu covered the first 300 miles of a trip going at 60 mph and the last hundred going at 40 mph. What was his average spee
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Answer:
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 scores for the univerisity A, and we know that:
Let Y the scores for the univerisity B, and we know that:
We select a sample size of size n=2, and since the distirbution for X is normal then the distribution for the sample mean would be given by:
And for the univeristy B we select a sample of n=3
Since both sample means are normally distributed then the difference is also normal distributed with the following parameters:
And we want this probability:
And we can use the z score given by:
And if we replace we got :
And if we find the probability using the normla standard table or excel we got: