Answer: 228 students
Step-by-step explanation:
Since the results for the standardized test are normally distributed, we would apply the formula for normal distribution which is expressed as
z = (x - µ)/σ
Where
x = test reults
µ = mean score
σ = standard deviation
From the information given,
µ = 1700 points
σ = 75 points
We want to find the probability of students expected to score above 1850 points. It is expressed as
P(x > 1850) = 1 - P(x ≤ 1850)
For x = 1850,
z = (1850 - 1700)/75 = 150/75 = 2
Looking at the normal distribution table, the probability corresponding to the z score is 0.97725
P(x > 1850) = 1 - 0.97725 = 0.02275
If 10,000 students take the exam, then the number of students you would expect to score above 1850 points is
0.02275 × 10000 = 228 students
Answer:
Question 18: 453,600
Step-by-step explanation:
Let the boxes be Box 1, Box 2, Box 3.
consider the 3 white balls. They can be all of them in one box:
(3, 0, 0) (3 in Box 1, 0 in box 2 and 0 in box 0)
(0, 3, 0)
(0, 0, 3)
We can have 2 in one box, and 1 in one of the remaining boxes:
(2, 0, 1)
(2, 1, 0)
(0, 2, 1)
(1, 2, 0)
(0, 1, 2)
(1, 0, 2)
and there is only one way: (1, 1, 1) to place one white ball in each box
In total there are: 3+6+1=10 ways to place the white balls. Similarly there are 10 ways to place the black ones.
Since every placement of the white balls can be combined with any placement of the black balls, there are 10*10=100 ways to place the 3white balls and the 3 black bals in the boxes.
Answer: 100
