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3 years ago

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Assume that women's heights are normally distributed with a mean given by mu equals 62.5 in, and a standard deviation given by

sigma equals 2.5 in. (a) If 1 woman is randomly selected, find the probability that her height is less than 63 in. (b) If 35 women are randomly selected, find the probability that they have a mean height less than 63 in. (a) The probability is approximately nothing. (Round to four decimal places as needed.) (b) The probability is approximately nothing. (Round to four decimal places as needed.)

1 answer:

kirza4 [7]3 years ago

6 0

Answer: a) The probability is approximately = 0.5793

b) The probability is approximately=0.8810

Step-by-step explanation:

Given : Mean : $\mu= 62.5\text{ in}$

Standard deviation : $\sigma = \text{2.5 in}$

a) The formula for z -score :

$z=\dfrac{x-\mu}{\dfrac{\sigma}{\sqrt{n}}}$

Sample size = 1

For x= 63 in. ,

$z=\dfrac{63-62.5}{\dfrac{2.5}{\sqrt{1}}}=0.2$

The p-value = $P(z$

$0.5792597\approx0.5793$

Thus, the probability is approximately = 0.5793

b) Sample size = 35

For x= 63 ,

$z=\dfrac{63-62.5}{\dfrac{2.5}{\sqrt{35}}}\approx1.18$

The p-value = $P(z$

$= 0.8809999\approx0.8810$

Thus , the probability is approximately=0.8810.

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Use Euler's method with step size 0.2 to estimate y(1), where y(x) is the solution of the initial-value problem y' = x2y − 1 2 y

irina [24]

Answer:

Therefore the value of y(1)= 0.9152.

Step-by-step explanation:

According to the Euler's method

y(x+h)≈ y(x) + hy'(x) ....(1)

Given that y(0) =3 and step size (h) = 0.2.

$y'(x)= x^2y(x)-\frac12y^2(x)$

Putting the value of y'(x) in equation (1)

$y(x+h)\approx y(x) +h(x^2y(x)-\frac12y^2(x))$

Substituting x =0 and h= 0.2

$y(0+0.2)\approx y(0)+0.2[0\times y(0)-\frac12 (y(0))^2]$

$\Rightarrow y(0.2)\approx 3+0.2[-\frac12 \times3]$ [∵ y(0) =3 ]

$\Rightarrow y(0.2)\approx 2.7$

Substituting x =0.2 and h= 0.2

$y(0.2+0.2)\approx y(0.2)+0.2[(0.2)^2\times y(0.2)-\frac12 (y(0.2))^2]$

$\Rightarrow y(0.4)\approx 2.7+0.2[(0.2)^2\times 2.7- \frac12(2.7)^2]$

$\Rightarrow y(0.4)\approx 1.9926$

Substituting x =0.4 and h= 0.2

$y(0.4+0.2)\approx y(0.4)+0.2[(0.4)^2\times y(0.4)-\frac12 (y(0.4))^2]$

$\Rightarrow y(0.6)\approx 1.9926+0.2[(0.4)^2\times 1.9926- \frac12(1.9926)^2]$

$\Rightarrow y(0.6)\approx 1.6593$

Substituting x =0.6 and h= 0.2

$y(0.6+0.2)\approx y(0.6)+0.2[(0.6)^2\times y(0.6)-\frac12 (y(0.6))^2]$

$\Rightarrow y(0.8)\approx 1.6593+0.2[(0.6)^2\times 1.6593- \frac12(1.6593)^2]$

$\Rightarrow y(0.6)\approx 0.8800$

Substituting x =0.8 and h= 0.2

$y(0.8+0.2)\approx y(0.8)+0.2[(0.8)^2\times y(0.8)-\frac12 (y(0.8))^2]$

$\Rightarrow y(1.0)\approx 0.8800+0.2[(0.8)^2\times 0.8800- \frac12(0.8800)^2]$

$\Rightarrow y(1.0)\approx 0.9152$

Therefore the value of y(1)= 0.9152.

4 0

3 years ago

In the book Essentials of Marketing Research, William R. Dillon, Thomas J. Madden, and Neil H. Firtle discuss a research proposa

MakcuM [25]

Answer:

Null hypothesis: $p_{1} = p_{2}$

Alternative hypothesis: $p_{1} \neq p_{2}$

$z=\frac{0.179-0.15}{\sqrt{0.17(1-0.17)(\frac{1}{140}+\frac{1}{60})}}=0.500$

$p_v =2*P(Z>0.500)=0.617$

So the p value is a very low value and using any significance level for example $\alpha=0.05, 0,1,0.15$ always $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can say the two proportions NOT differs significantly.

Step-by-step explanation:

Data given and notation

$X_{1}=25$ represent the number of homeowners who would buy the security system

$X_{2}=9$ represent the number of renters who would buy the security system

$n_{1}=140$ sample 1

$n_{2}=60$ sample 2

$p_{1}=\frac{25}{140}=0.179$ represent the proportion of homeowners who would buy the security system

$p_{2}=\frac{9}{60}= 0.15$ represent the proportion of renters who would buy the security system

z would represent the statistic (variable of interest)

$p_v$ represent the value for the test (variable of interest)

Concepts and formulas to use

We need to conduct a hypothesis in order to check if the two proportions differs , the system of hypothesis would be:

Null hypothesis: $p_{1} = p_{2}$

Alternative hypothesis: $p_{1} \neq p_{2}$

We need to apply a z test to compare proportions, and the statistic is given by:

$z=\frac{p_{1}-p_{2}}{\sqrt{\hat p (1-\hat p)(\frac{1}{n_{1}}+\frac{1}{n_{2}})}}$ (1)

Where $\hat p=\frac{X_{1}+X_{2}}{n_{1}+n_{2}}=\frac{25+9}{140+60}=0.17$

Calculate the statistic

Replacing in formula (1) the values obtained we got this:

$z=\frac{0.179-0.15}{\sqrt{0.17(1-0.17)(\frac{1}{140}+\frac{1}{60})}}=0.500$

Statistical decision

For this case we don't have a significance level provided $\alpha$ , but we can calculate the p value for this test.

Since is a two sided test the p value would be:

$p_v =2*P(Z>0.500)=0.617$

So the p value is a very low value and using any significance level for example $\alpha=0.05, 0,1,0.15$ always $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can say the two proportions NOT differs significantly.

6 0

3 years ago

when the driver is in the empty truck, the mass is 2948.35 kilogram. the mass of 1 box of paper is 22.5 kilograms. the driver de

marishachu [46]

Answer:

0 boxes minimum

Step-by-step explanation:

The mass of the truck and paper must satisfy ...

22.5b + 2948.35 ≤ 4700 . . . . total truck mass cannot exceed bridge limits

22.5b ≤ 1751.65

b ≤ 77.85

The driver can take a minimum of 0 boxes and a maximum of 77 boxes of paper over the bridge.

_____

The question asks for the <em>minimum</em>. We usually expect such a question to ask for the <em>maximum</em>.

7 0

3 years ago

James knows that when he walks, he takes about 120

Tpy6a [65]

Answer:

speed of James is: 3.75 miles/hour.

Step-by-step explanation:

We need to find the speed of James in miles per hour(mi/hr)

we know that 1 mile=5280 feet

James takes 120 steps in 1 minute so he will cover 120×60 steps in 1 hour.

i.e. he takes 7200 steps in 1 hour.

also each step of James=2.75 feet

total distance covered by James in 1 hour=2.75×7200 feet=19800 feet

$19800feet=\frac{19800}{5280} miles=3.65miles$

hence speed of James= (distance covered by james in 1 hour)/1 hour

speed of James=3.75 miles/hour.

Thanks!!

Mark me brainliest!

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7 0

3 years ago

Read 2 more answers

WILL GIVE BRAINLIEST IF CORRECT ANSWER!!!

Rom4ik [11]

Answer : 2√3

<u>Given </u><u>:</u><u>-</u>

A equilateral triangle with side length 4.

<u>To </u><u>Find</u><u> </u><u>:</u><u>-</u>

The value of x in the given figure.

As we know that in a equilateral triangle , perpendicular bisector , angle bisector and median coincide with each other .

So the perpendicular drawn in the figure will bisect the given side .
Therefore the value of each half will be 4/2 = 2 .

Now we may use Pythagoras theorem as ,

→ AB² = BC² + AC²

→ 4² = 2² + x²

→ 16 = 4 + x²

→ x² = 16-4

→ x² = 12

→ x =√12 = √{ 3 * 2²}

→ x = 2√3

<u>Hence </u><u>the</u><u> required</u><u> answer</u><u> is</u><u> </u><u>2</u><u>√</u><u>3</u><u> </u><u>.</u>

I hope this helps.

3 0

2 years ago