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Scorpion4ik [409]
3 years ago
6

The amount of time Ricardo spends brushing his teeth follows a Normal distribution with unknown mean and standard deviation. Ric

ardo spends less than one minute brushing his teeth about 40% of the time. He spends more than two minutes brushing his teeth 2% of the time. Use this information to determine the mean and standard deviation of this distribution
Mathematics
1 answer:
Papessa [141]3 years ago
7 0
Let X denote the number of minutes spent brushing his teeth, and let \mu be the mean and \sigma the standard deviation for this distribution.

\mathbb P(X

The z-score corresponding to this probability is approximately z=-0.2533, which means

\dfrac{1-\mu}\sigma=-0.2533\iff\mu-0.2533\sigma=1

Next, (note the sign change)

\mathbb P(X>2)=0.02\implies\mathbb P(X\le2)=\mathbb P\left(\dfrac{X-\mu}\sigma\le\dfrac{2-\mu}\sigma\right)=0.98

The corresponding z-score is approximately z=2.0538, so you have

\dfrac{2-\mu}\sigma=2.0538\iff\mu+2.0538\sigma=2

Solving the two equations for \mu and \sigma, you'll find that the mean is approximately \mu=1.1098 and the standard deviation is approximately \sigma=0.4334.
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<u>Part 1) </u>To find the measure of ∠A in ∆ABC, use

we know that

In the triangle ABC

Applying the law of sines

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in this problem we have

\frac{a}{sin\ A}=\frac{b}{sin\ theta}\\ \\a*sin\ theta=b*sin\ A\\ \\ sin\ A=\frac{a*sin\ theta}{b} \\ \\ A=arc\ sin (\frac{a*sin\ theta}{b})

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<u>the answer  Part 1) is</u>

Law of Sines

<u>Part 2) </u>To find the length of side HI in ∆HIG, use

we know that

In the triangle HIG

Applying the law of cosines

g^{2}=h^{2}+i^{2}-2*h*i*cos\ G

In this problem we have

g=HI

G=angle Beta

substitute

HI^{2}=h^{2}+i^{2}-2*h*i*cos\ Beta

HI=\sqrt{h^{2}+i^{2}-2*h*i*cos\ Beta}

therefore

<u>the answer Part 2) is</u>

Law of Cosines

3 0
2 years ago
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Answer:

Step-by-step explanation:

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3 years ago
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Answer:

In Section 6.1, we introduced the logarithmic functions as inverses of exponential functions and

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Step-by-step explanation:

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2 years ago
Volume of cylinder pi 3.14 r 8mm h 42mm
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Answer:

V≈8.44×10-6m³

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