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2 years ago

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The average score of 100 students taking a statistics final was 70 with a standard deviation of 7. Assuming a normal distributio

n, what test score separates the top 5% of the students from the lower 95% of students?

1 answer:

MakcuM [25]2 years ago

6 0

Answer:

Hence, the answer is $x>71.1515$

Step-by-step explanation:

We have,

$n=100,\mu=70,\sigma=7$

The top percentage of the students is $5\%$

The lower percentage of the students is $95\%$

The lowest $95\%$ is the left area from the normal distribution table, the area $0.95$ lies in the z-table

$z=1.645$ from the z- table

$P(z1.645)=0.05\\z>1.645$

$\frac{x-\mu}{\frac{\sigma}{\sqrt{\mu}} } >1.645\\x>1.645\times \frac{\sigma}{\sqrt{n}} +\mu$

$>1.645\times \frac{7}{\sqrt{100}} +70$

$\Rightarrow x>71.1515$

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Classify the pair of angles. Then find the value of x.

sleet_krkn [62]

Answer:

3) x = 50, vertical angles.

4) x = 20, supplementary angles

5) x = 14, complimentary angles

Step-by-step explanation:

<h3>3)</h3>

<em>vertical angles.</em>

<em>vertical angles are equal.</em>

<em>so, you can make this equation:</em>

67 = x + 17

<em>subtract 17 from both sides of the equation</em>

67 - 17 = x + 17 - 17

67 - 17 = x

50 = x

<h3>4)</h3>

<em>supplementary angles</em>

<em>supplementary angles add up to 180</em>

<em>so, you can make this equation:</em>

7x + 40 = 180

<em>subtract 40 from both sides of the equation</em>

7x + 40 - 40 = 180 - 40

7x = 180 - 40

7x = 140

<em>divide both sides by 7</em>

7x/7 = 140/7

x = 140/7

x = 20

<h3>5)</h3>

<em>complimentary angles</em>

<em>complimentary angles add up to 90</em>

<em>so, you can make this equation:</em>

4x + 34 = 90

<em>subtract 34 from both sides of the equation</em>

4x + 34 - 34 = 90 - 34

4x = 90 - 34

4x = 56

<em>divide both sides by 4</em>

4x/4 = 56/4

x = 56/4

x = 14

8 0

2 years ago

Consider the following hypothesis test.H0:μ1−μ2=0 Ha:μ1−μ2≠0The following results are for two independent samples taken from the

Julli [10]

Answer:

a) $z =\frac{104-106}{\sqrt{\frac{8.4^2}{80} +\frac{7.6^2}{70}}}= -1.53$

b) $p_v =2*P(z$

c) Since the p value is higher than the significance level provided we have enogh evidence to FAIL to reject the null hypothesis and we can't conclude that the true means are different at 5% of significance

Step-by-step explanation:

Information given

$\bar X_{1}= 104$ represent the mean for 1

$\bar X_{2}= 106$ represent the mean for 2

$\sigma_{1}= 8.4$ represent the population standard deviation for 1

$\sigma_{2}= 7.6$ represent the population standard deviation for 2

$n_{1}=80$ sample size for the group 1

$n_{2}=70$ sample size for the group 2

z would represent the statistic

Hypothesis to test

We want to check if the two means for this case are equal or not, the system of hypothesis would be:

H0: $\mu_{1}=\mu_{2}$

H1: $\mu_{1} \neq \mu_{2}$

The statistic would be given by:

$z =\frac{\bar X_1-\bar X_2}{\sqrt{\frac{\sigma^2_1^2}{n_1} +\frac{\sigma^2_2^2}{n_2}}}=$ (1)

Part a

Replacing we got:

$z =\frac{104-106}{\sqrt{\frac{8.4^2}{80} +\frac{7.6^2}{70}}}= -1.53$

Part b

The p value would be given by this probability:

$p_v =2*P(z$

Part c

Since the p value is higher than the significance level provided we have enogh evidence to FAIL to reject the null hypothesis and we can't conclude that the true means are different at 5% of significance

6 0

2 years ago

(15 POINTS!) The graph shows the distance a ghost crab can run over time the D equals the distance in meters and the t equal the

Maru [420]

Answer:

B. d = 5/3t

Step-by-step explanation:

The complete question is shown in the figure attached with.

We need to find the equation of direct variation using the graph. The general equation for a direction variation is:

y = kx

In this case, the variable along x axis is time in seconds i.e. "t" and the variable along y axis is distance in meters i.e. "d". So, the equation for this case would be:

d = kt

We need to find the value of "k" to complete this equation. For this we can use any point from the graph and substitute it in the above equation. From the graph we can see that the distance covered for time = 3 seconds is 5 meters. Substituting t =3 and d = 5 in above equation, we get:

5 = 3k

k = 5/3

Using the value of k in the above equation, we get:

$d=\frac{5}{3}t$

Therefore, option B gives the correct answer

7 0

2 years ago

What is the exact solution to the equation 4^5x=3^(x-2)<br> list the steps to get the answer

scoray [572]

Answer: x = -0.377

Step-by-step explanation:

We have the equation:

4^(5*x) = 3^(x - 2)

Now we can use the fact that:

Ln(A^x) = x*Ln(A)

Then we can apply Ln(.) to both sides of the equation to get:

Ln(4^(5*x)) = Ln(3^(x - 2))

(5*x)*Ln(4) = (x - 2)*Ln(3)

(5*x)*Ln(4) - x*Ln(3) = -2*Ln(3)

x*(5*Ln(4) - Ln(3)) = -2*Ln(3)

x = -2*Ln(3)/(5*Ln(4) - Ln(3)) = -0.377

6 0

2 years ago

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viva [34]

Answer:

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2 years ago