We have been given that the ages of students in a school are normally distributed with a mean of 15 years and a standard deviation of 2 years.
We are asked to find the percentage of students that are between 14 and 18 years old.
First of all, we will find z-score corresponding to 14 and 18 using z-score formula.
Similarly, we will find the z-score corresponding to 18.
Now we will find the probability of getting a z-score between and
that is
.
Using normal distribution table, we will get:
Let us convert into percentage.
Therefore, approximately of the students are between 14 and 18 years old.
Answer:
Step-by-step explanation:
Given is a statement that e is a positive number
This can also be written as:
(a) All positive numbers have positive square root.
(b) For every positive number e, there is a square root for e
(c) For every positive number, there is a positive number r such that
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Explanation:
The given piecewise function is
At first piecewise functions may be strange confusing things, but they aren't so bad. I like to think of it like this: f(x) is a function that changes its identity based on what the input x is. We have three situations
In a sense, we have three different functions but they are combined somehow.
If x is smaller than 3, then we go for the first definition. Or if x is between 3 and 8, then we go for the second definition. Or if x is larger than 8, then we go for the third definition.
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f(-5) means f(x) when x = -5. We see that -5 is smaller than 3, so x = -5 makes x < 3 true. We'll use the first definition
f(x) = -4x+3
f(-5) = -4(-5)+3
f(-5) = 20+3
f(-5) = 23
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Now the input is x = 12. This is larger than 8. In other words, x = 12 makes x > 8 true. We'll use the third definition
f(x) = 3x^2+1
f(12) = 3(12)^2+1
f(12) = 3(144)+1
f(12) = 432+1
f(12) = 433
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Side notes: