2. The population of a school is 800 students and is increasing at a rate of 2% per year. Write an
1 answer:
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Answer:
a) For this case we can use this:
So the range of lengths would be 32.1 and 46.5 since on the middle of these two values we have 1-0.0015-0.0015=0.997 or 99.7 % of the values.
b)
And using the complement rule we have:
Step-by-step explanation:
Previous concepts
The empirical rule, also known as three-sigma rule or 68-95-99.7 rule, "is a statistical rule which states that for a normal distribution, almost all data falls within three standard deviations (denoted by σ) of the mean (denoted by µ)".
Let X the random variable who represent the variable of interest.
From the problem we have the mean and the standard deviation for the random variable X.
So we can assume
On this case in order to check if the random variable X follows a normal distribution we can use the empirical rule that states the following:
• The probability of obtain values within one deviation from the mean is 0.68
• The probability of obtain values within two deviation's from the mean is 0.95
• The probability of obtain values within three deviation's from the mean is 0.997
So we have the following probabilities using this rule:
Part a
For this case we can use this:
So the range of lengths would be 32.1 and 46.5 since on the middle of these two values we have 1-0.0015-0.0015=0.997 or 99.7 % of the values.
Part b
For this casee we want this probability:
And using the complement rule we have:
Answer:
a) We can remove the complete rotations around the unitary circle like this, because we know that one complete revolution is equivalent to :
For this case we know that
So then
b) We can remove the complete rotations around the unitary circle like this, because we know that one complete revolution is equivalent to :
For this case we know that
And we know that is on the III quadrant since is equivalent to 210 degrees. And on the III quadrant the cosine is negative. So then
c) For this case that any factor of the sin function is equal to 0.
So from definition of tan we have this:
Step-by-step explanation:
a. sin (17pi / 4 )
We can remove the complete rotations around the unitary circle like this, because we know that one complete revolution is equivalent to :
For this case we know that
So then
b. cos (19pi / 6 )
We can remove the complete rotations around the unitary circle like this, because we know that one complete revolution is equivalent to :
For this case we know that
And we know that is on the III quadrant since is equivalent to 210 degrees. And on the III quadrant the cosine is negative. So then
c. tan(450pi)
For this case that any factor of the sin function is equal to 0.
So from definition of tan we have this: