Entry to a certain university is determined by a national test. the scores on this test are normally distributed with a mean of 500 and a standard deviation of 100. tom wants to be admitted to this university and he knows that he must score better than at least 70% of the students who took the test. tom takes the test and scores 585. will he be admitted to this university?

Tom will be admitted to the university.

Explanation:

To find out if Tom will be admitted to the university, we must calculate whether he was better than 70% of the students who took the test. For this we will do the following calculation:

Z = (x − μ) / σ

μ = 500

σ = 100

x = 585

Z = (585−500) /100=0.85

Now we must find the probability:

P (Z <0.85) = P (Z <0) + P (0 <Z <0.85)

P (Z <0) = 0.5

P (0 <Z <0.85) = 0.3023

(from Z-table) ---> = 0.5 + 0.3023 = 0.8023.

This means that Tom was better than 80.23% of the students who took the exam, so he will be admitted to the university.

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