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MariettaO [177]
3 years ago
6

If the heights of 300 students are normally distributed with mean 68.0 inches and standard deviation 3.0 inches, how many studen

ts have heights (a) greater than 72 inches, (b) less than or equal to 64 inches, (c) between 65 and 71 inches inclusive, (d) equal to 68 inches? assume the measurements to be recorded to the nearest inch.
Mathematics
1 answer:
Lunna [17]3 years ago
3 0
Given:
μ = 68 in, population mean
σ = 3 in, population standard deviation

Calculate z-scores for the following random variable and determine their probabilities from standard tables.

x = 72 in:
z = (x-μ)/σ = (72-68)/3 = 1.333
P(x) = 0.9088

x = 64 in:
z = (64 -38)/3 = -1.333
P(x) = 0.0912

x = 65 in
z = (65 - 68)/3 = -1
P(x) = 0.1587

x = 71:
z = (71-68)/3 = 1
P(x) = 0.8413

Part (a)
For x > 72 in, obtain
300 - 300*0.9088 = 27.36

Answer: 27

Part (b)
For x ≤ 64 in, obtain
300*0.0912 = 27.36

Answer: 27

Part (c)
For 65 ≤ x ≤ 71, obtain
300*(0.8413 - 0.1587) = 204.78

Answer: 204

Part (d)
For x = 68 in, obtain
z = 0
P(x) = 0.5
The number of students is
300*0.5 = 150

Answer: 150

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Usimov [2.4K]

Answer:

Step-by-step explanation:

All of these numbers can be divided by 2, 3, 5, 7, 11, 13...

There is no whole number if you want to divide each number.

121 only goes into 1, 11, and 121. No other numbers have 11

45/2 = 22.5

45/3 = 15

45/5 = 9

2470/2 = 1235

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2470/5 = 494

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121/5 = 24.2

4 0
3 years ago
A container has 3 apple juice boxes, 4 grape juice boxes and 5 orange juice boxes. Alex picks one juice box, drinks it and then
Eduardwww [97]

Hey!

Grape over total: \frac{4}{12}

After he drinks 1, there will be 1 less. That means it will be over 11

Orange over total: \frac{5}{11}

Now multiply the fractions

\frac{4}{12} \times \frac{5}{11} = \frac{20}{132} \rightarrow \frac{10}{66} \rightarrow \frac{5}{33}

That means the probability is: \frac{5}{33}

Good luck and hope this helps! :)

4 0
3 years ago
Gabriel wants to paint the model. How
enyata [817]

Answer:

<h2>The area of the base is 144 square inches.</h2><h2>The area of each triangular face is 66 square inches.</h2><h2>Grabiel needs 408 square inches of paint.</h2>

Step-by-step explanation:

The complete problem is attached.

Notice that the figure is a square pyramid, where its base dimensions are 12 inches by 12 inches, which represents an area of

B=12 \times 12 = 144 \ in^{2}

The slant height of the pyramid is 11 inches, which allow us to find the area of each triangle face

A=\frac{1}{2}bh =\frac{1}{2}(12)(11)= 66 \ in^{2}

But there are four triangle faces, so A_{faces} =4(66)=264 \ in^{2}.

Therefore, the area of each triangular face is 66 square inches.

So, the total surface area would be the sum

S=144+264=408 \ in^{2}

Therefore, Gabriel needs 408 square inches to paint the whole model.

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3 years ago
Two brothers have a total age of 28 if one brother is older by 20 years how old is the second brother
svlad2 [7]

Answer:

8

Step-by-step explanation:

Total meaning addition, you would use the opposite operation to find the answer.  

28 - 20 = 8

And to check your work you would add;

20 + 8 = 28

which is the brothers total combined age.  

6 0
3 years ago
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