A town spends 43% of its annual budget on education.
2 answers:
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Answer:
The probability that <em>X</em> is less than 42 is 0.1271.
Step-by-step explanation:
The random variable <em>X </em>follows a Normal distribution.
The mean and standard deviation are:
E (X) = <em>μ</em> = 50.
SD (X) = <em>σ</em> = 7.
A normal distribution is continuous probability distribution.
The Normal probability distribution with mean µ and standard deviation σ is given by,
To compute the probability of a Normal random variable we first standardize the raw score.
The raw scores are standardized using the formula:
These standardized scores are known as <em>z</em>-scores and they follow normal distribution with mean 0 and standard deviation 1.
Compute the probability of (X < 42) as follows:
*Use a <em>z</em>-table for the probability.
Thus, the probability that <em>X</em> is less than 42 is 0.1271.
The normal curve is shown below.
Answer:
M(x₄ ,y₄) = (-3.5 , 0.5) and
N (x₅ ,y₅) = ( -1 , -0.5 )
Step-by-step explanation:
Let the endpoint coordinates for the mid segment of △PQR that is parallel to PQ be
M(x₄ ,y₄) and N(x₅ ,y₅) such that MN || PQ
point P( x₁ , y₁) ≡ ( -3 ,3 )
point Q( x₂ , y₂) ≡ (2 , 1 )
point R( x₂ , y₂) ≡ (-4 , -2)
To Find:
M(x₄ ,y₄) = ? and
N (x₅ ,y₅) = ?
Solution:
We have Mid Point Formula as
As M is the mid point of PR and N is the mid point of RQ so we will have
Substituting the given value in above equation we get
∴
∴
Similarly,
∴
∴
∴ M(x₄ ,y₄) = (-3.5 , 0.5) and
N (x₅ ,y₅) = ( -1 , -0.5 )