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The number of square feet per house is normally distributed with a population standard deviation of 154 square feet and an unkno

11111nata11111 [884]

Answer: (1500.66,1599.34)

Step-by-step explanation:

Confidence interval for population mean:

$\overline{x}\pm z^*\dfrac{\sigma}{\sqrt{n}}$

,where $\overline{x}$ = Sample mean , n= Sample size, z* = critical two tailed z-value , $\sigma$ = population standard deviation.

As per given , we have

n= 16

$\sigma = 154$ square feet

$\overline{x}= 1550$ square feet

$\alpha= 1-0.80 = 0.20$

Critical z-value = $z_{\alpha/2}=z_{0.2/2}=z_{0.1}=1.2815$

Confidence interval for population mean:

$1550\pm (1.2815)\dfrac{154}{\sqrt{16}}\\\\ = 1550\pm (1.2815)\dfrac{154}{4}\\\\= 1550\pm 49.33775\\\\ =(1550-49.33775,\ 1550+49.33775)\\\\\approx (1500.66,\ 1599.34)$

Required confidence interval: (1500.66,1599.34)

6 0

3 years ago

A random sample of 20 purchases showed the sample mean of $48.77 and the sample standard deviation s is $17.58. How large is the

laila [671]

Answer:

Step-by-step explanation:

Given data

Sample Mean (M): $48.77

Sample Size (n): 20

Standard Deviation (σ) : $17.58

Confidence Level: 80%

we know that z*-Values for 80% Confidence Levels is 1.28

the expression for margin of error is given bellow\

MOE= z*σ/√n

We can now substitute into the expression and solve for the MOE as

MOE= 1.28*17.58/√20

MOE= 22.502/4.47

MOE= 5.03

The margin of error for a 80 % confidence interval is $5.03

3 0

3 years ago

How do you simplify this expression step by step?

nataly862011 [7]

$\bf \textit{Pythagorean Identities} \\\\ sin^2(\theta)+cos^2(\theta)=1\implies cos^2(\theta)=1-sin^2(\theta) \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \cfrac{csc(\theta )-sin(\theta )}{cos(\theta )}\implies \cfrac{~~\frac{1}{sin(\theta )}-sin(\theta )~~}{cos(\theta )}\implies \cfrac{~~\frac{1-sin^2(\theta )}{sin(\theta )}~~}{cos(\theta )}$

$\bf \cfrac{1-sin^2(\theta )}{sin(\theta )}\cdot \cfrac{1}{cos(\theta )}\implies \cfrac{\stackrel{cos(\theta )}{\begin{matrix} cos^2(\theta ) \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}} }{sin(\theta )}\cdot \cfrac{1}{\begin{matrix} cos(\theta ) \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix} }\implies \cfrac{cos(\theta )}{sin(\theta )}\implies cot(\theta )$