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2 years ago

8

A simple random sample is drawn from a normally distributed population, and when making a statistical inference about the popula

tion mean, the margin of error is found to be 5.9 at a 95% level of confidence. If the mean of the sample is 18.7, what is the 95% confidence interval for the population mean?

2 answers:

DiKsa [7]2 years ago

3 0

<span>To find the confidence interval, add and subtract the margin of error from the mean. With mean 18.7 and margin of error 5.9, you have 95% confidence the answer is between 12.8 and 24.6.</span>

V125BC [204]2 years ago

3 0

Answer:

B. 18.7 ± 9.7

Step-by-step explanation:

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Mopeds (small motorcycles with an engine capacity below 50 cm3) are very popular in Europe because of their mobility, ease of op

Alex17521 [72]

Answer:

a) $P(X$

And we can find this probability using the normal standard table or excel and we got:

$P(z$

b) $P(X>48)=P(\frac{X-\mu}{\sigma}>\frac{48-\mu}{\sigma})=P(Z>\frac{48-46.8}{1.75})=P(z>0.686)$

And we can find this probability using the complement rule, the normal standard table or excel and we got:

$P(z>0.686)=1- P(Z$

c) $P(46.8-1.5*1.75$

And we can find this probability with this difference:

$P(-1.5$

And in order to find these probabilities we can use tables for the normal standard distribution, excel or a calculator.

$P(-1.5$

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Part a

Let X the random variable that represent the velocities of a population, and for this case we know the distribution for X is given by:

$X \sim N(46.8,1.75)$

Where $\mu=46.8$ and $\sigma=1.75$

We are interested on this probability

$P(X$

And the best way to solve this problem is using the normal standard distribution and the z score given by:

$z=\frac{x-\mu}{\sigma}$

If we apply this formula to our probability we got this:

$P(X$

And we can find this probability using the normal standard table or excel and we got:

$P(z$

Part b

$P(X>48)=P(\frac{X-\mu}{\sigma}>\frac{48-\mu}{\sigma})=P(Z>\frac{48-46.8}{1.75})=P(z>0.686)$

And we can find this probability using the complement rule, the normal standard table or excel and we got:

$P(z>0.686)=1- P(Z$

Part c

$P(46.8-1.5*1.75$

And we can find this probability with this difference:

$P(-1.5$

And in order to find these probabilities we can use tables for the normal standard distribution, excel or a calculator.

$P(-1.5$

6 0

2 years ago

The population of a Midwestern city decays exponentially. If the population decreased from 900,000 to 800,000 from 2003 to 2005,

olga55 [171]

Hello.<span><span> </span><span>
<span><span>
-------
Let 2003 be the zero year; then 2005 is the three year, and 2008 the 5 year.
---------------
P = ab^x
---
P(3) = ab^3 = 800000
P(0) = ab^0 = 900000

---
a = 900000
Solve for "b"::
b^3 = 8/9
b = 2/cbrt(9)
----
Equation::
P(x) = 900000^x
----
Ans: P(5) = 900000

Have a nice day</span></span></span></span>

4 0

2 years ago

If cos Θ = square root 2 over 2 and 3 pi over 2 < Θ < 2π, what are the values of sin Θ and tan Θ?

KIM [24]

Answer:

The answer is

$sin(\theta)=-\frac{\sqrt{2}}{2}$

$tan(\theta)=-1$

Step-by-step explanation:

we know that

$tan(\theta)=\frac{sin(\theta)}{cos(\theta)}$

$sin^{2}(\theta)+cos^{2}(\theta)=1$

In this problem we have

$cos(\theta)=\frac{\sqrt{2}}{2}$

$\frac{3\pi}{2}$

so

The angle $\theta$ belong to the third or fourth quadrant

The value of $sin(\theta)$ is negative

Step 1

Find the value of $sin(\theta)$

Remember

$sin^{2}(\theta)+cos^{2}(\theta)=1$

we have

$cos(\theta)=\frac{\sqrt{2}}{2}$

substitute

$sin^{2}(\theta)+(\frac{\sqrt{2}}{2})^{2}=1$

$sin^{2}(\theta)=1-\frac{1}{2}$

$sin^{2}(\theta)=\frac{1}{2}$

$sin(\theta)=-\frac{\sqrt{2}}{2}$ ------> remember that the value is negative

Step 2

Find the value of $tan(\theta)$

$tan(\theta)=\frac{sin(\theta)}{cos(\theta)}$

we have

$sin(\theta)=-\frac{\sqrt{2}}{2}$

$cos(\theta)=\frac{\sqrt{2}}{2}$

substitute

$tan(\theta)=\frac{-\frac{\sqrt{2}}{2}}{\frac{\sqrt{2}}{2}}$

$tan(\theta)=-1$

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nevsk [136]

The cost of the watch originally cost $1,640.31

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2 years ago

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Shalnov [3]

Answer:

StartFraction 1.55 over 1 EndFraction = StartFraction 3.5 over x EndFraction

Step-by-step explanation:

1 = 1.55

x = 3.5

1.55/1 =3.5/x

1.55/1 = 3.5/x correctly shows the equivalent ratios

5 0

2 years ago

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