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?
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.
Standard deviation is a measure of the amount of variation of data.
Here, we have a low standard deviation of 100 as compare with the mean value of 500. Low standard deviation indicates that the values are close to the mean of the set, while a high standard deviation indicates that the values are spread out over a wider range.
It means that most candidates scores are centred around 500 mark. Tom had 585, which is greater than 500 mark and 85 mark higher than the mean value.
