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mixer [17]
3 years ago
7

20000 students took a standardized math test. The scores on the test are normally distributed, with a mean score of 85 and a sta

ndard deviation of 5. About how many students scored between 90 and 95?
Mathematics
1 answer:
Tpy6a [65]3 years ago
7 0

Answer: 2718

Step-by-step explanation:

Given: Mean score = 85

Standard deviation = 5

Let x be the score of a random student that follows normal distribution.

Then, the probability that a student scored between 90 and 95 will be

P(90< x < 95)\\\\=P(\dfrac{90-85}{5}

The number of students scored between 90 and 95 = 0.1359 x (Total students)

= 0.1359 (20000)

= 2718

Hence, The number of students scored between 90 and 95 = 2718

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A town is designing a rectangular park that will be 600 feet wide by 1000 feet long. On a scale drawing, the dimensions of the p
KonstantinChe [14]

Scale drawing takes scaled versions of original lengths. The actual length of the swing set area of the park is 25 ft long and 100 ft wide

<h3>How are scale drawings formed?</h3>

For a particular scale drawing, it is already specified that all the measurements' some constant scaled version will be taken. For example, let the scale be K feet to s inches.

Then it means

\rm 1\:  ft : \dfrac{s}{k}\:  in.

All feet measurements will then be multiplied by s/k to get the drawing's corresponding lengths.

For the given case, it is given that

Real dimension of a rectangular park : 600 ft by 1000 ft

In drawing, it was of 12 inches by 20 inches.

Let the scale that the drawing is using be k feet to s inches, then

\rm 1\:  ft : \dfrac{s}{k}\:  in.

Since it is given that 600 ft : 12 inches and 1000 ft : 20 inches, thus, we get:

\rm 1\:  ft : \dfrac{s}{k}\:  in.\\\\600 \: ft = \dfrac{600\times s}{k} \: in. =  12 \: in.\\\\\dfrac{600 \times s}{k} = 12\\\\\dfrac{s}{k} = \dfrac{12}{600} = 0.02

Thus, every feet is reduced 0.02 times in drawing.

Now,

it is given that in drawing, the rectangular area for swing sets is 0.5 inch to 2 inch.

Let its real length was L and real width was W. Then we have:
\rm L \times 0.02 = 0.5 \\\\L = \dfrac{0.5}{0.02} = 25 \:\\\\W \times 0.02 = 2 \\W = \dfrac{2}{0.02} = 100

Since these are only magnitudes, and unit was converted from feet to inches, so we have L = 25 feet and W = 100 feet

Thus,

The actual length of the swing set area of the park is 25 ft long and 100 ft wide

Learn more about scaling here:
brainly.com/question/8765466

6 0
2 years ago
Use the following problem to answer questions 8 and 9. A television manufacturer has three locations where it is finally assembl
Nonamiya [84]

Answer:

The probability of finding a non-defective television is 0.9815.

Step-by-step explanation:

We are given that a television manufacturer has three locations where it is finally assembled. Plants A, B, and C supply 65%, 15%, and 20% respectively of the televisions used by the manufacture.

Quality control has determined that 1.5% produced by Plant A are defective, while plants B and C have 2.5% defective products.

Let Probability that Plant A supply televisions = P(A) = 0.65

Probability that Plant B supply televisions = P(B) = 0.15

Probability that Plant C supply televisions = P(C) = 0.20

<em>Also, let D = event that television is defective</em>

Probability that television is defective given that it is supplied by Plant A = P(D/A) = 0.015

Probability that television is defective given that it is supplied by Plant B = P(D/B) = 0.025

Probability that television is defective given that it is supplied by Plant C = P(D/C) = 0.025

<u>Now, to find the probability of finding a non-defective television firstly we will find the probability of a defective television.</u>

<em>Probability of a defective television is given by;</em>

   =  P(A) \times P(D/A) + P(B) \times P(D/B) + P(C) \times P(D/C)  

   =  0.65 \times 0.015 + 0.15 \times 0.025 + 0.20 \times 0.025  

   =  0.00975 + 0.00375 + 0.005

   =  0.0185

Now, <em><u>probability of finding a non-defective television</u></em> = 1 - Pro<em>bability of a defective television</em>

Probability of finding a non-defective television = 1 - 0.0185

                                                                                   = 0.9815

<em>Therefore, the probability of finding a non-defective television is 98.15%.</em>

8 0
4 years ago
You've decided to buy a potted plant to brighten up your room. The gardening store near you offers 4 different plants that can l
Marrrta [24]

Answer:

diagram a and b

Step-by-step explanation:

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4 years ago
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Given the equation y = 3x − 4, what is the value of x when y = 5? A) 3 B) 6 C) 9 D) 12
timurjin [86]

Answer:

3

Step-by-step explanation:

the equation would be 5 = 3(3) - 4

which is 9 - 4 = 5

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4 years ago
The area of a baseball field bounded by home plate, first base, second base, and third base is a square. If a player at first ba
JulsSmile [24]

Answer:

ta side from one base to next has  length of x. so we know each side has length x and  the shape they make is a square. This means we are only searching for the diagonal of a square. remember that a diagonal forms and isoscoles right triangle with the 2 sides being equal and the diagonal as the hypotenuse. Using  pythagoream theorem we can say

a^2 + b^2 = c^2 all side lengths are x so we can put x in for a and b  to get

x^2 + x^2 = c^2

2x^2 = c^2

c = x * squareroot(2)

so if the length between bases is 90 ft

c = 90 ft * squareroot(2)

c = 127.28 ft

Step-by-step explanation:

6 0
2 years ago
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