What is the answer

X has a normal distribution with the given mean and standard deviation. Find the indicated probability. (Round your answer to fo

lapo4ka [179]

Answer:

0.6247

Step-by-step explanation:

The formula for calculating a Z-score is Z = (X - μ)/σ,

where x is the raw score

μ is the population mean

σ is the population standard deviation.

From the question,

μ = 51, σ = 10. We are to find P(36 ≤ X ≤ 56)

Step 1

Find the Probability of X ≤ 36

μ = 51, σ = 10

Z = (X - μ)/σ

Z = 36 - 51/ 10

Z = -15/10

Z = -1.5

We find the Probability of Z = -1.5 from Z-Table

P(X <36) = P(X = 36) = P(Z = -1.5)

= 0.066807

Step 2

Find the Probability of X ≤ 56

μ = 51, σ = 10

Z = (X - μ)/σ

Z = 56 - 51/ 10

Z = 5/10

Z = 0.5

We find the Probability of Z = 0.5 from Z-Table:

P(X < 56) = P(X = 56) = P(Z = 0.5)= 0.69146

Step 3

Find P(36 ≤ X ≤ 56)

P(36 ≤ X ≤ 56) = P(X ≤ 56) - P(X ≤ 36)

= P( Z = 0.5) - P(Z = -1.5)

= 0.69146 - 0.066807

= 0.624653

Approximately to 4 decimal places , P(36 ≤ X ≤ 56) = 0.6247

7 0

3 years ago

Can anyone help? grnheujghniuhwseruhuiwheriuh (Sorry about the letters just trying to get past the 20 words.)

babymother [125]

Answer:

8!!!

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers

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

Adam bought a fish aquarium worth $3,000 in the first week of the year. Its value depreciates by 3% per week. What will the valu

LenKa [72]

=0.75 times 3000=2250

7 0

2 years ago

Match the y-coordinates with their corresponding pairs of x-coordinates on the unit circle. the x coordinates to choose from are

vaieri [72.5K]

Of the four x-coordinates to choose only 1/√(11) belongs can belong to the unit circle.

The other three x-coordinates are greater than 1, then they are out of the unit circle.

The unit circle formula is x^2 +y^2 = 1

Then to find the y-coordinate given the x-coordinate you can solve for y from that formula:

y^2 = 1 - x^2

y = (+/-)√(1-x^2)

Substitute the value of x

y = (+/-)√{1 - [1/√(11)]^2} = (+/-) √{(1 - 1/11} =(+/-) √ {(11 -1)/11 =(+/-)√(10/11) ≈ +/- 0.95

6 0

2 years ago

What is the answer ​

What is the answer