In: Math

Consider a normal population distribution with the value of σ known.

(a) What is the confidence level for the interval \(\bar{x} \pm 2.81 \sigma / \sqrt{n} ?\) (Round your answer to one decimal place.) \(\%\)

(b) What is the confidence level for the interval \(\bar{x} \pm 1.43 \sigma / \sqrt{n} ?\) (Round your answer to one decimal place.) \(\%\)

(c) What value of \(z_{\alpha / 2}\) in the CI formula below results in a confidence level of \(99.7 \% ?\) (Round your answer to two decimal places.)

\(\left(\bar{x}-z_{u / 2} \cdot \frac{\sigma}{\sqrt{n}}, \bar{x}+z_{u / 2} \cdot \frac{\sigma}{\sqrt{n}}\right)\)

\(z_{a / 2}=\)

(d) Answer the question posed in part (c) for a confidence level of \(75 \%\). (Round your answer to two decimal places.) \(z_{u / 2}=\)

a)z(two tailed)=+/-2.81

P(z<2.81)-P(z<-2.81)=0.995 or 99.5%

So,confidence level,c=**99.5%**

b)z(two tailed)=+/-1.43

P(z<1.43)-P(z<-1.43)=0.847 or **84.7%**

So,confidence level,c=**84.7%**

c)c=0.997

alpha=1-0.997=0.003

alpha/2=0.0015

z=normsinv(0.0015) or
normsinv(1-0.0015)=**+/-2.97**

**2.97**

d)c=0.75

alpha=1-0.75=0.25

alpha/2=0.125

z=normsinv(0.125) or
normsinv(1-0.125)=**+/-1.15**

**1.15**

Consider a normal population distribution with the value of \(\sigma\) known.(a) What is the confidence level for the interval \(\bar{x} \pm 2.88 \sigma / \sqrt{n} ?\) (Round your answer to one decimal place.)\(\%\)(b) What is the confidence level for the interval \(\bar{x} \pm 1.47 \sigma / \sqrt{n} ?\) (Round your answer to one decimal place.) \(\%\)(c) What value of \(z_{\alpha / 2}\) in the CI formula below results in a confidence level of \(99.7 \% ?\) (Round your answer to...

1.Consider a population of values has a normal distribution with
μ=193.1 and σ=89.5. You intend to draw a random sample of size n.
The boxes are labeled #1-12. Complete the table by writing the
number that goes in the box with the corresponding number. Round to
four decimal places.
n
Sample means
Sample Standard Deviations
2
1.
2.
5
3.
4.
10
5.
6.
20
7.
8.
50
9.
10.
100
11.
12.
2. Describe what happens to the sample...

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A population of values has a normal distribution with μ = 231.5
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, Find the probability that a single randomly selected value is
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241.3) =
Find the probability that a sample of size n=19n=19 is randomly
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four decimals.
P(M > 241.3) =

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Enter your answers as numbers accurate to 1 decimal place.
Answers obtained using exact z-scores or z-scores rounded to 3
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A population of values has a normal distribution with μ = 49.1
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A population of values has a normal distribution with μ = 240.5
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.
Find the probability that a single randomly selected value is
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Find the probability that a sample of size n = 131 is randomly
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A population of values has a normal distribution with μ = 107.5
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P ( 106.4 < X < 110 ) =
b.) Find the probability that a sample of size n = 133 is
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A population of values has a normal distribution with μ = 180.2
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Find the probability that a single randomly selected value is
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