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I am Lyosha [343]

3 years ago

15

your manager believes that 43% of the company's orders come from first-time customers. A random sample of 98 orders will be used

to estimate the proportion of first-time-customers. What is the probability that the sample proportion is between 0.33 and 0.46?

1 answer:

Tpy6a [65]3 years ago

5 0

Answer: 0.7030

Step-by-step explanation:

Given : The population proportion for company's orders come from first-time customers : p=0.43

Sample size : n= 98

The test statistic for population proportion:-

$z=\dfrac{\hat{p}-p}{\sqrt{\dfrac{p(1-p)}{n}}}$

For , $\hat{p}=0.33$

$z=\dfrac{0.33-0.43}{\sqrt{\dfrac{0.43(1-0.43)}{98}}}\approx-2.00$

For , $\hat{p}=0.46$

$z=\dfrac{0.46-0.43}{\sqrt{\dfrac{0.43(1-0.43)}{98}}}\approx0.60$

$\text{The p-value =}P(-2.00$

Hence, the probability that the sample proportion is between 0.33 and 0.46 is 0.7030.

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Each day, Robin commutes to work by bike with probability 0.4 and by walking with probability 0.6. When biking to work injuries

kvasek [131]

Answer:

64.65% probability of at least one injury commuting to work in the next 20 years

Step-by-step explanation:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

$P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}
$

In which

x is the number of sucesses

e = 2.71828 is the Euler number

$\mu$ is the mean in the given interval.

Each day:

Bikes to work with probability 0.4.

If he bikes to work, 0.1 injuries per year.

Walks to work with probability 0.6.

If he walks to work, 0.02 injuries per year.

20 years.

So

$\mu = 20*(0.4*0.1 + 0.6*0.02) = 1.04$

Either he suffers no injuries, or he suffer at least one injury. The sum of the probabilities of these events is decimal 1. So

$P(X = 0) + P(X \geq 1) = 1$

We want $P(X \geq 1)$ . Then

$P(X \geq 1) = 1 - P(X = 0)$

In which

$P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}
$

$P(X = 0) = \frac{e^{-1.04}*1.04^{0}}{(0)!} = 0.3535
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$P(X \geq 1) = 1 - P(X = 0) = 1 - 0.3535 = 0.6465$

64.65% probability of at least one injury commuting to work in the next 20 years

3 0

2 years ago

Rewrite the following integral in spherical coordinates.

lora16 [44]

In cylindrical coordinates, we have $r^2=x^2+y^2$ , so that

$z = \pm \sqrt{2-r^2} = \pm \sqrt{2-x^2-y^2}$

correspond to the upper and lower halves of a sphere with radius $\sqrt2$ . In spherical coordinates, this sphere is $\rho=\sqrt2$ .

$1 \le r \le \sqrt2$ means our region is between two cylinders with radius 1 and $\sqrt2$ . In spherical coordinates, the inner cylinder has equation

$x^2+y^2 = 1 \implies \rho^2\cos^2(\theta) \sin^2(\phi) + \rho^2\sin^2(\theta) \sin^2(\phi) = \rho^2 \sin^2(\phi) = 1 \\\\ \implies \rho^2 = \csc^2(\phi) \\\\ \implies \rho = \csc(\phi)$

This cylinder meets the sphere when

$x^2 + y^2 + z^2 = 1 + z^2 = 2 \implies z^2 = 1 \\\\ \implies \rho^2 \cos^2(\phi) = 1 \\\\ \implies \rho^2 = \sec^2(\phi) \\\\ \implies \rho = \sec(\phi)$

which occurs at

$\csc(\phi) = \sec(\phi) \implies \tan(\phi) = 1 \implies \phi = \dfrac\pi4+n\pi$

where $n\in\Bbb Z$ . Then $\frac\pi4\le\phi\le\frac{3\pi}4$ .

The volume element transforms to

$dx\,dy\,dz = r\,dr\,d\theta\,dz = \rho^2 \sin(\phi) \, d\rho \, d\theta \, d\phi$

Putting everything together, we have

$\displaystyle \int_0^{2\pi} \int_1^{\sqrt2} \int_{-\sqrt{2-r^2}}^{\sqrt{2-r^2}} r \, dz \, dr \, d\theta = \boxed{\int_0^{2\pi} \int_{\pi/4}^{3\pi/4} \int_{\csc(\phi)}^{\sqrt2} \rho^2 \sin(\phi) \, d\rho \, d\phi \, d\theta} = \frac{4\pi}3$

4 0

2 years ago

A rectangular state flag has dimensions 7 feet by 5 1/2 feet. How long is its diagonal? Round your answer to the nearest tenth i

slamgirl [31]

The formula for a diagonal of a rectangle is <span>√w^2+h^2, with w and h being the width and height. Plug in your numbers to get </span><span>√7^2+5.5^2. Simplify that into </span><span>√49+30.25, then to </span><span>√79.25. Use your calculator to get 8.9022. The diagonal is 8.9 feet.</span>

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3 years ago

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VMariaS [17]

Answer:

$(y-z)^{2}$

Step-by-step explanation:

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3 years ago

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umka21 [38]

Answer:

40,000

Step-by-step explanation:

You want to start with the exponent and then multiply afterward in both of the equations.

8 x 10^-2:

10^-2 = 0.01

0.01 x 8 = 0.08

2 x 10^-6:

10^-6 = 0.000001

0.000001 x 2 = 0.000002

Obviously, you can see the relationship between 8 and 2 in the division. Now, you just divide 0.08 by 0.000002 and you get 40,000.

4 0

1 year ago