Scores on a recent national statistics exam were normally distributed with a mean of 82.2 and a standard deviation of 5.If the top 2.5% of test scores receive merit awards, what is the lowest score eligible for an award
Answers
Answer:
The lowest score eligible for an award is 92.
Step-by-step explanation:
When the distribution is normal, we use the z-score formula.
In a set with mean and standard deviation
, the zscore of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this question:
If the top 2.5% of test scores receive merit awards, what is the lowest score eligible for an award
The lowest score is the 100 - 2.5 = 97.5th percentile, which is X when Z has a pvalue of 0.975. So X when Z = 1.96. Then
The lowest score eligible for an award is 92.
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Answers
Final answer:
Cos(88°) can be estimated using the 3rd degree Taylor polynomial for cos(x) centered at a = π/2. The degrees need to be converted to radians, and by substituting into the polynomial, the cosine value to five decimal places is approximately 0.03490.
Explanation:
To estimate cos(88°) using the 3rd degree Taylor polynomial for cos(x) centered at a = π/2, we first need to convert 88 degrees to radians as cos(x) expects x in radians. 88 degrees is roughly 1.53589 radians. Now, substituting x = 1.53589 into the Taylor polynomial yields the estimate.
The given Taylor polynomial is represented as cos(x) = - (x - π/2) + 1/6 * (x - π/2)³. Substituting x with 1.53589, we get:
cos(1.53589) = - (1.53589 - π/2) + 1/6 * (1.53589 - π/2)³
To get the estimate correct to five decimal places, you calculate the above expression to get roughly 0.03490. Therefore, cos(88°) is approximately 0.03490.
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Final answer:
First, we convert the given angle 88° into radians, since standard trigonometrical functions take angles in radians. We then substitute this into the Taylor series given, keeping in mind the importance of the remainder term.
Explanation:
This problem deals with the concept of Taylor series approximation, which is a widely used method in mathematics to estimate the value of functions. The given Taylor polynomial approximates the cosine function. To estimate cos(88°), we first need to convert the angle from degrees to radians, because the standard trigonometric functions in mathematics take input in radians. Remember that 180° equals π radians. So 88° can be represented as (88/180)π radians.
Substitute this into the provided series − x − π/2 + 1/6 * (x − π/2)³ + R3(x). Be wary of the remainder term R3(x). This term ensures the correctness of the approximation on the interval of convergence. The closer x is to the center, the more accurate the approximation. In practical computations, you might need to take more terms into account to ensure sufficient accuracy to five decimal places in this case.
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Answers
Answer:
Step-by-step explanation:
the sum of the interior angles of a hexagon is 720 degrees. All sides are the same length (congruent) and all interior angles are the same size (congruent). To find the measure of the interior angles, we know that the sum of all the angles is 720 degrees.
Now,
102+146+158+120+124+x=720
or,650+x=720
or,x=70
Therefore The value of X is 70 degree.
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B.) (-3, 4) = "left 3 up 4" [ Option B, D ]
C.) (4, -3) = "right 4 down 3" [ Option E ]
Hope this helps!
Answers
Answer:
The answer is X∈∅
Step-by-step explanation: {=
h(x)=-49x-125
Answers
h(-67) = 3158
General Formulas and Concepts:
Order of Operations: BPEMDAS
- Substitution and Evaluation
Step-by-Step Explanation:
Step 1: Define
h(x) = -49x - 125
h(-67)
Step 2: Solve
1. Substitute: h(-67) = -49(-67) - 125
2. Multiply: h(-67) = 3283 - 125
3. Subtract: h(-67) = 3158