Answer: 2718
Step-by-step explanation:
Given: Mean score = 85
Standard deviation = 5
Let x be the score of a random student that follows normal distribution.
Then, the probability that a student scored between 90 and 95 will be
The number of students scored between 90 and 95 = 0.1359 x (Total students)
= 0.1359 (20000)
= 2718
Hence, The number of students scored between 90 and 95 = 2718
The dimension that would give the maximum area is 20.8569
<h3>How to solve for the maximum area</h3>
Let the shorter side be = x
Perimeter of the semi-circle is πx
Twice the Length of the longer side
Length =
Total area =
area of rectangle + area of the semi-circle.
Total area =
When we square it we would have
This gives
From here we divide by 2
The maximum side would be at
This gives us 20.8569
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