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?
yes he will be admitted.
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.
Therefore he has chances of getting admission.
Tom will be admitted to the 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.
σ=100 (standard deviation)
Tom does better than what percentage?
Tom got 585 marks
we will have to find how many students got less than 585
x<585 (find the probability)
converting the problem in standard form
P(0<Z<0.85)=0.3023 (from Z- table)
so the total probability=0.5+0.3023=0.8023
so Tom got more than 80.23% of students
where is the options
answer; i believe the correct answer is enlightenment;