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Mazyrski [523]
3 years ago
15

A humanities professor assigns letter grades on a test according to the following scheme. A: Top 12% of scores B: Scores below t

he top 12% and above the bottom 61% C: Scores below the top 39% and above the bottom 21% D: Scores below the top 79% and above the bottom 6% F: Bottom 6% of scores Scores on the test are normally distributed with a mean of 67.7 and a standard deviation of 7.8. Find the minimum score required for an A grade. Round your answer to the nearest whole number, if necessary.
Mathematics
1 answer:
allsm [11]3 years ago
3 0

Answer:

The minimum score required for an A grade is 77.

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

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, we have that:

\mu = 67.7, \sigma = 7.8

Find the minimum score required for an A grade.

Top 12% of scores get an A.

100-12 = 88th percentile.

The 88th percentile of scores is the minimum required for an A grade. This score is X when Z has a pvalue of 0.88. So X when Z = 1.175.

Z = \frac{X - \mu}{\sigma}

1.175 = \frac{X - 67.7}{7.8}

X - 67.7 = 7.8*1.175

X = 76.865

Rounding to the nearest whole number:

The minimum score required for an A grade is 77.

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3 years ago
Find the measure of angle 1
Lubov Fominskaja [6]
In ∆FDH, there are two slash marks in two of its legs. This indicates that this triangle is isosceles. If a triangle is isosceles, then it will have two congruent sides and therefore have two congruent angles.

In ∆FDH, angle D is already given to us as the measure of 80°. We can find out the measure of the other angles of this triangle by using the equation:

80 + 2x = 180

Subtract 80 from both sides of the equation.

2x = 100

Divide both sides by 2.

x = 50

This means that angle F and angle H in ∆FDH both measure 50°.

Now, moving over to the next smaller triangle in the picture is ∆DHG. In this triangle, there are also two legs that are congruent which once again indicates that this triangle is isosceles.

First, we have to solve for angle DHG and we do that by using the information obtained from solving for the angles of the other triangle.

**In geometry, remember that two or more consecutive angles that form a line will always be supplementary; the angles add up to 180°.**

In this case angle DHF and angle DHG are consecutive angles which form a linear pair. So, we can use the equation:

Angle DHF + Angle DHG = 180°

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Angle DHG = 130°.

Now that we know the measure of one angle in ∆DHG, we can use the same method as the previous step for solving the missing angles. Use the equation:

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x = 25

The other two missing angles of ∆DHG are 25°. This means that the measure of angle 1 is also 25°.

Solution: 25°
8 0
3 years ago
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4 0
2 years ago
HELP NEEDED !!!!
Fofino [41]
The answer is Letter D - 84%

68% of the data is within +/- 1 SD from the mean = 59 to 7195% of the data is within +/- 2 SDs from the mean = 53 to 7799.7% of the data is within +/- 3 SDs from the mean = 47 to 83

The whole 68% (59 - 71) scored below 71. Since the data are evenly distributed, we'll get the 32% (100 - 68) outside the range of 68% and divide it by 2 and add the quotient to the original 68% so that we'll get the total data below 71.
   100 - 68 = 32
   32 / 2 = 16
   16 + 68 = 84
7 0
3 years ago
How do you write 72% as a fraction in simplest form?
Step2247 [10]
72% = 72/100

72/100=36/50=18/25 
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3 years ago
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