Ask question

Ask question

All categories

3 years ago

6

You measure the lifetime of a random sample of 64 tires of a certain brand. The sample mean is x¯=50 months. Suppose that the li

fetimes for tires of this brand follow a Normal distribution, with unknown mean µ and standard deviation σ=5 months, then a 99% confidence interval for µ is:

1 answer:

Anni [7]3 years ago

3 0

Answer:

(48.3875, 51.6125)

Step-by-step explanation:

At 99% level of significance

$\alpha=1-0.99=0.01$

$Z_{a\lpha /2}=0.01/2=0.005$

From the normal standard deviation table $Z_{a\lpha /2}=2.33$

Considering that

$\bar x$ ± $Z_{a\lpha /2} \frac {\sigma}{\sqrt{n}}$ =50± $2.33\frac {5}{\sqrt {64}}$

50±2.33(0.625)=50±1.6125=(48.3875, 51.6125)

Therefore, there’s 99% confidence that the mean lifetime of a certain brand of tires is between 48.3875 and 51.6125

You might be interested in

Megan expects to save an average of 5 dollars per week from her babysitting earnings. The relationship between time and the amou

Novosadov [1.4K]

Answer:

(0,0), (0.5, 2.5)

Step-by-step explanation:

I had gotten that correct!

5 0

3 years ago

Read 2 more answers

if I had a triangle and one side was 45 degrees and the other side was 2k and the other side was k then what is the value of k?

DanielleElmas [232]

K = 45 180=45+2(45)+45

6 0

3 years ago

Covert 4 centimeters into meters .

frutty [35]

4 ÷ 100 = 0.04 meters

3 0

3 years ago

Read 2 more answers

Please can you help me?

Gennadij [26K]

Answer:

$\large\boxed{C)\ \dfrac{3}{4}}$

Step-by-step explanation:

$\text{We know:}\ P(A')=1-P(A)\\\\\text{Therefore}\\\\P(A)-3\cdot P(A')=0\iff P(A)-3\cdot(1-P(A))=0\\\\\text{use the distributive property}\ a(b+c)=ab+ac\\\\P(A)+(-3)(1)+(-3)(-P(A))=0\\\\P(A)-3+3P(A)=0\qquad\text{add 3 from both sides}\\\\P(A)+3P(A)=3\\\\4P(A)=3\qquad\text{divide both sides by 4}\\\\P(A)=\dfrac{3}{4}$

4 0

3 years ago

The base and sides of a container is made of wood panels. The container does not have a lid. The base and sides are rectangular.

vfiekz [6]

Answer:

Minimum surface area = $70.77 cm^2$

Step-by-step explanation:

We are given that

Width of container=x cm

Length of container=2x cm

Volume of container= $54 cm^3$

We have to find the minimum surface areas that this container will have.

Volume of container= $l\times b\times h$

$x\times 2x\times h=54$

$2x^2h=54$

$h=\frac{54}{2x^2}=\frac{27}{x^2}$

Surface area of container= $2(b+l)h+lb$

Because the container does not have lid

Surface area of container= $S=2(2x+x)\times \frac{27}{x^2}+2x\times x$

$S=\frac{162}{x}+2x^2$

Differentiate w.r.t x

$\frac{dS}{dx}=-\frac{162}{x^2}+4x$

$\frac{dx^n}{dx}=nx^{n-1}$

Substitute $\frac{dS}{dx}=0$

$-\frac{162}{x^2}+4x=0$

$4x=\frac{162}{x^2}$

$x^3=\frac{162}{4}=40.5$

$x^3=40.5$

$x=(40.5)^{\frac{1}{3}}$

$x=3.4$

Again differentiate w.r.t x

$\frac{d^2S}{dx^2}=\frac{324}{x^3}+4$

Substitute x=3.4

$\frac{d^2S}{dx^2}=\frac{324}{(3.4)^3}+4=12.24>0$

Hence, function is minimum at x=3.4

Substitute x=3.4

Then, we get

Minimum surface area = $\frac{162}{(3.4)}+2(3.4)^2=70.77 cm^2$

8 0

3 years ago