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Rzqust [24]
3 years ago
15

Suppose the scores on an exam are normally distributed with a mean μ = 75 points, and standard deviation σ = 8 points. Suppose t

hat the top 4% of the exams will be given an A+. In order to be given an A+, an exam must earn at least what score?
Mathematics
1 answer:
alexandr402 [8]3 years ago
6 0

Answer:

89.008

Step-by-step explanation:

z = (x– mean)/ standard deviation

x = z * standard deviation + mean

Now, z value for the top 4% of the exams (which is the same as getting a score below the 96%) has to be found using a z table.

In this case z = 1.751

x = 1.751 * 8 + 75

x = 89.008

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A rancher wants to fence in an area of 1500000 square feet in a rectangular field and then divide it in half with a fence down t
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Answer:

6000 ft

Step-by-step explanation:

Let length of rectangular field=x

Breadth of rectangular field=y

Area of rectangular field=1500000 square ft

Area of rectangular field=l\times b

Area of rectangular field=x\time y

1500000=xy

y=\frac{1500000}{x}

Fencing used ,P(x)=x+x+y+y+y=2x+3y

Substitute the value of y

P(x)=2x+3(\frac{1500000}{x})

P(x)=2x+\frac{4500000}{x}

Differentiate w.r.t x

P'(x)=2-\frac{4500000}{x^2}

Using formula:\frac{dx^n}{dx}=nx^{n-1}

P'(x)=0

2-\frac{4500000}{x^2}=0

\frac{4500000}{x^2}=2

x^2=\frac{4500000}{2}=2250000

x=\sqrt{2250000}=1500

It is always positive because length is always positive.

Again differentiate w.r.t x

P''(x)=\frac{9000000}{x^3}

Substitute x=1500

P''(1500)=\frac{9000000}{(1500)^3}>0

Hence, fencing is minimum at x=1 500

Substitute x=1 500

y=\frac{1500000}{1500}=1000

Length of rectangular field=1500 ft

Breadth of rectangular field=1000 ft

Substitute the values

Shortest length of fence used=2(1500)+3(1000)=6000 ft

Hence, the shortest length of fence that the rancher can used=6000 ft

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4 years ago
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