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LekaFEV [45]
3 years ago
13

A university dean is interested in determining the proportion of students who receive some sort of financial aid. Rather than ex

amine the records for all students, the dean randomly selects 200 students and finds that 118 of them are receiving financial aid. Use a 99% confidence interval to estimate the true proportion of students on financial aid, with limits rounded to four decimal places.
Mathematics
1 answer:
schepotkina [342]3 years ago
6 0

Answer:

Step-by-step explanation:

Mean = np

Where

n = number of students

p = probability of success

n = 200

p = 118/200 = 0.59

mean = 200 × 0.59 = 118

Standard deviation, s = √npq

q = 1 - p = 1 - 0.59

q = 0.41

s = √(200 × 0.59 × 0.41)

s = √48.38 = 6.956

For a confidence level of 99%, the corresponding z value is 2.58. This is determined from the normal distribution table.

We will apply the formula

Confidence interval

= mean ± z ×standard deviation/√n

It becomes

118 ± 2.58 × 6.956/√200

= 118 ± 2.58 × 0.492

= 118 ± 1.2694

The lower end of the confidence interval is 118 - 1.2694 = 116.7306

The upper end of the confidence interval is 118 + 1.2694 = 119.2694

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Answer:

The value is E(x) =  1.25

Step-by-step explanation:

From the question we are told that

The number of cans is n = 4

The number of can that are empty is N = 3

The number of can filled with water is k = 1

The number number of sets of cans is w = 5

Generally probability of detecting the correct can is mathematically represented as

p  =  \frac{k}{n}

=> p  =  \frac{1}{4}

=> p  = 0.25

Generally probability of not detecting the correct can is mathematically represented as

q =  1- p

q =  1- 0.25

q = 0.75

Generally the number of cans expected of the farmer to correctly identify by chance is mathematically represented as

E(x) =  w  *  p

=> E(x) =  5  * 0.75

=> E(x) =  1.25

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Answer:

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tino4ka555 [31]

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Step-by-step explanation:

6 0
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A manufacturer is planning to sell a new product at the price of 210 dollars per unit and estimates that if x thousand dollars i
sattari [20]

Answer:

Development costs: $2757

Promotion costs: $3155

Step-by-step explanation:

This might seem like a two-variable problem, but in actuality it's not - because the demand function is a sum of two components, each being independent and using only one variable, we can solve for the two separately.

Moreover, the price per unit and cost per unit is constant, so each product yields exactly $80 ($210 - $130).

Let's solve separately.

We need to maximize:

$80 * 160y/(y+4) - 1000y = $12800 * y/(y+4) - $1000*y

$80 * 170x/(x+7) - 1000x = $13600 * x/(x+7) - $1000*x

Let's go:

$12800 * y/(y+4) - $1000*y = $12800 * (1 - 4/(y+4)) - $1000y = $12800 - $51200/(y+4) - $1000*y

we analyze the derivative. $12800 is a constant, so we can skip it. Derivative of 1/(y+4) is -(y+4)^-2, derivative of $1000y is $1000.

deriv = $51200/(y+4)/(y+4) - $1000

We find the changepoints by analyzing $51200/(y+4)/(y+4) - $1000 = $0. We don't need to worry about y+4 = 0 because we cannot spend negative money on development/advertisement.

(y+4)^2 = $51.2

y+4 ~= 7.155417528 (or -y-4 = 7.1554... but it doesn't make sense because negative budget so we don't analyze).

y ~= 3.155417528

lastly, we should check that it's actually a maximum there - but it is, the original function goes to negative infinity.

rounding $1000y to the nearest dollar gives us $3155

Let's do the same for x:

$13600 * x/(x+7) - $1000*x = $13600 * (1 - 7/(x+7)) - $1000x = $13600 - $95200/(x+7) - $1000*x

deriv = $95200/(x+7)/(x+7) - $1000

$95200/(x+7)/(x+7) - $1000 = $0

(x+7)^2 = 95.2

(x+7) ~= 9.75704873412

x ~= 2.75704...

rounding $1000x to the nearest dollar yields $2757

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