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Free_Kalibri [48]
2 years ago
4

Given a normal random variable X with mean 20 and variance 9, and a random sample of size n taken from the distribution, what sa

mple size n is necessary in order that P(19.9 ≤ X ≤ 20.1) = 0.95?
Mathematics
1 answer:
DanielleElmas [232]2 years ago
6 0
Interval at 95% = mean +/- Z*sd/Sqrt(n)

It can be noted that: error = 20.1-20=20-19.9 = 0.1

Therefore,
0.1= Z*sd/sqrt (n) => n = {Z*sd/0.1}^2

At 95% confidence interval, Z = 1.96, sd = sqrt (variance) = sqrt (9) = 3

Then,
Necessary sample size is,
n = {1.96*3/0.1}^2 = 3457.44 =3,458
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Grant plans to evaporate enough water from 22 gallons of a 16% ammonia solution to make a 24% ammonia solution. Which equation c
Paha777 [63]
First lets write down our starting conditions:

we have 22 gallons and it has 16% of ammonia

16% of 22 gallons is
A = 16/100*22 = 3,52 gallons

Now since only watter is evaporating that means that in second scenario after some watter evaporated there is still 3,52 gallons of ammonia. But now those 3,52 gallons of ammonia represent 24% of total mixture. So now we go other way. 
24 % is 3,52 gallons
100% is x gallons

x = 100/24*3,52 = 14.667 gallons

That means that he has to evaporate 
22 - 14.6667 = 7,333 gallons of water.
7 0
2 years ago
Find the number a such that the line x = a bisects the area under the curve y = 1/x2 for 1 ≤ x ≤ 4. 8 5​ (b) find the number b s
IceJOKER [234]

a. We're looking for a such that

\displaystyle\int_1^a\frac{\mathrm dx}{x^2}=\int_a^4\frac{\mathrm dx}{x^2}

-\dfrac1x\bigg|_{x=1}^{x=a}=-\dfrac1x\bigg|_{x=a}^{x=4}

1-\dfrac1a=\dfrac1a-\dfrac14

\dfrac54=\dfrac2a\implies\boxed{a=\dfrac85}

b. Integrating with respect to y will make things easier.

y=\dfrac1{x^2}\implies x=\dfrac1{\sqrt y}

(where we take the positive square root because we know x>0)

Now we want to find b such that

\displaystyle\int_0^b\frac{\mathrm dy}{\sqrt y}=\int_b^1\frac{\mathrm dy}{\sqrt y}

2\sqrt y\bigg|_{y=0}^{y=b}=2\sqrt y\bigg|_{y=b}^{b=1}

2\sqrt b=2-2\sqrt b

4\sqrt b=2\implies\boxed{b=\dfrac14}

3 0
2 years ago
Question 1(Multiple Choice Worth 1 points)
tester [92]

The correct answer is d15

7 0
2 years ago
The slope of a line is 2. The y-intercept of the line is -6. Which statements accurately describe how to graph the function
Law Incorporation [45]
It’s a. Start at the y intercept and rise over run to the next point.
8 0
2 years ago
Hadi earned $120.00 from his job yesterday. Today he expects to earn 15% less than yesterday and tomorrow he expects to earn 15%
alexira [117]
Yesterday Hadi earned: $120

Today he will earn: $120*85% = $102
(You times the amount yesterday by 85% because you want to find the 15% less of 100% of the amount he's earned yesterday. Therefore, to find 15% less than yesterday you multiply it by 85% (100% - 15%) )

Tomorrow he will earn: $102*115% = $117.30
(Same thing here, however you are finding 15% more than 100% today. Therefore, you multiply the amount he earned today it by 115% (100% + 15%) )

To find the amount he earns for the three days you must add the amount earned of yesterday, today and tomorrow earned from the working above.

Therefore, Hadi expects to earn:
Yesterday + Today + Tomorrow = 120 + 102 + 117.30 = $339.3


3 0
2 years ago
Read 2 more answers
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