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Schach [20]
3 years ago
9

Scores on an exam follow an approximately bell shaped distribution with a mean of 76.4 and a standard deviation of 6.1 points. A

pproximately, what percentage of the data is between 64.2 points and 88.6 points?
a) 68%
b) 95%
c) 99.7%
d) 50%
Mathematics
1 answer:
Crazy boy [7]3 years ago
6 0

Answer:

b) 95%

Step-by-step explanation:

We have been given that scores on an approximately bell shaped distribution with a mean of 76.4 and a standard deviation of 6.1 points. We are asked to find the percentage of the data that is between 64.2 points and 88.6 points.

First of all, we will find z-scores of each data point as:

z=\frac{x-\mu}{\sigma}

z=\frac{64.2-76.4}{6.1}

z=\frac{-12.2}{6.1}

z=-2

Let us find z-score corresponding to normal score 88.6.

z=\frac{88.6-76.4}{6.1}

z=\frac{12.2}{6.1}

z=2

To find the percentage of the data is between 64.2 points and 88.6 points, we need to find area under a normal distribution curve that lie within two standard deviation of mean.

The empirical rule of normal distribution states that approximately 95% of data points fall within two standard deviation of mean, therefore, option 'b' is the correct choice.

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The base of a triangle exceeds the height by 9 centimeters. If the area is 56 square centimeters, find the length of the base an
shepuryov [24]

Answer:

The height of the triangle is 7cm and the base is 16cm

Step-by-step explanation:

First of all we have to know the formula to calculate area of ​​a triangle

a = area = 56

b = base

h = heigth

a = (b * h)/2

we replace the known values and we make 2 equations

56cm² = (b * h)/2

b = h + 9cm

we replace b by (h + 9cm) in the first equation

56cm² = (h + 9cm * h)/2

56cm² * 2 = h² + 9h

0 = h² + 9h - 112cm²

we use bhaskara formula:

(-b (±) √ (b² - 4ac) ) / 2a

we replace with the known values

h = (-9 (±) √ (9² - 4*1*(-112) ) ) / 2*1

h = (-9 (±) √ (81 + 448) ) ) / 2

h = (-9 (±) √529) /2

h = (-9 (±) 23)/2

h1 = (-9 + 23) / 2

h1 = 14 / 2

h1 = 7

h2 = (-9 - 23) / 2

h2 = -32 / 2

h2 = -16

The height of the triangle is 7cm and the base is 16cm

8 0
3 years ago
Which statement is true about the expressions below?
Zielflug [23.3K]
Is there a attachment because I don’t see anything
7 0
3 years ago
A. Find PR in the diagram <br> b. Find the perimeter of quadrilateral PQRS
Elan Coil [88]

Answer:

Step-by-step explanation:

The quadrilateral has 4 sides and only two of them are equal.

A) to find PR, we will consider the triangle, PRQ.

Using cosine rule

a^2 = b^2 + c^2 - 2abcos A

We are looking for PR

PR^2 = 8^2 + 7^2 - 2 ×8 × 7Cos70

PR^2 = 64 + 49 - 112 × 0.3420

PR^2 = 113 - 38.304 = 74.696

PR = √74.696 = 8.64

B) to find the perimeter of PQRS, we will consider the triangle, RSP. It is an isosceles triangle. Therefore, two sides and two base angles are equal. To determine the length of SP,

We will use the sine rule because only one side,PR is known

For sine rule,

a/sinA = b/sinB

SP/ sin 35 = 8.64/sin110

Cross multiplying

SPsin110 = 8.64sin35

SP = 8.64sin35/sin110

SP = (8.64 × 0.5736)/0.9397

SP = 5.27

SR = SP = 5.27

The perimeter of the quadrilateral PQRS is the sum of the sides. The perimeter = 8 + 7 + 5.27 + 5.27 = 25.54 cm

6 0
3 years ago
The rectangle below has an area of x^2-144x
dangina [55]

Answer:

37x, 12

Step-by-step explanation:

8 0
4 years ago
the perimeter of a rectangle is 20 units. The length of the rectangle is the distance from(-2,6) to (5,6) What is the width in u
DIA [1.3K]

Answer:

3 units.

Step-by-step explanation:

We can calculate the length, since it only moves on the "x" axis, since on the "y" axis, it remains the same.

We know that between -2 to 5, there are 7 units. 2 + 5 = 7.

Therefore this would be the length.

We know that the perimeter is equal to:

p = 2 * w + 2 * l

P = 20

20 = 2 * w + 2 * 7

2 * w = 20 - 14

w = 6/2

w = 3

therefore, the width value is 3 units.

4 0
3 years ago
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