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Based on the model N(11541154,8686) describing steer weights, what are the cutoff values for a) the highest 10% of the we

yaroslaw [1]

Answer:

a) x = 1225.68

b) x = 1081.76

c) 1109.28 < x < 1198.72

Step-by-step explanation:

Given:

- Th random variable X for steer weight follows a normal distribution:

X~ N( 1154 , 86 )

Find:

a) the highest 10% of the weights?

b) the lowest 20% of the weights?

c) the middle 40% of the weights?

Solution:

a)

We will compute the corresponding Z-value for highest cut off 10%:

Z @ 0.10 = 1.28

Z = (x-u) / sd

Where,

u: Mean of the distribution.

s.d: Standard deviation of the distribution.

1.28 = (x - 1154) / 86

x = 1.28*86 + 1154

x = 1225.68

b)

We will compute the corresponding Z-value for lowest cut off 20%:

-Z @ 0.20 = -0.84

Z = (x-u) / sd

-0.84 = (x - 1154) / 86

x = -0.84*86 + 1154

x = 1081.76

c)

We will compute the corresponding Z-value for middle cut off 40%:

Z @ 0.3 = -0.52

Z @ 0.7 = 0.52

[email protected] < x < [email protected]

-.52*86 + 1154 < x < 0.52*86 + 1154

1109.28 < x < 1198.72

7 0

3 years ago

5/6+5/6 show your work

Umnica [9.8K]

10/6 = 1 2/3 This is because 5 + 5 =10/6 Divide 19 by six. This gives you 1 2/3

6 0

3 years ago

The elevations of four points below sea level are -47 feet, -24 feet, -8 feet, and -18 feet. The elevation of the point closest

Gelneren [198K]

The elevations of four points below sea level are -47 feet, -24 feet, -8 feet, and -18 feet.

The elevation of the point closest to sea level is feet

-8 ft

elevation of the point farthest from sea level is feet.

-47 ft

closet to sea level to farthest to sea level

-8ft , -18ft , -24ft , -47ft

4 0

3 years ago

According to a Washington Post-ABC News poll, 331 of 502 randomly selected U.S. adults interviewed said they would not be bother

k0ka [10]

Answer:

$z=\frac{0.659 -0.5}{\sqrt{\frac{0.5(1-0.5)}{502}}}=7.124$

$p_v =P(z>7.124)=5.24x10^{-13}$

So the p value obtained was a very low value and using the significance level given $\alpha=0.05$ we have $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 5% of significance the proportion of interest is significantly higher than 0.5.

Step-by-step explanation:

Data given and notation

n=502 represent the random sample taken

X=331 represent the adults that said they would not be bothered if the NAtional security agency

$\hat p=\frac{331}{502}=0.659$ estimated proportion of people who would not be bothered if the NAtional security agency

$p_o=0.5$ is the value that we want to test

$\alpha=0.01$ represent the significance level

Confidence=99% or 0.99

z would represent the statistic (variable of interest)

$p_v$ represent the p value (variable of interest)

Concepts and formulas to use

We need to conduct a hypothesis in order to test the claim that the true proportion is higher than the majority of 0.5:

Null hypothesis: $p\leq 0.5$

Alternative hypothesis: $p > 0.5$

When we conduct a proportion test we need to use the z statistic, and the is given by:

$z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}$ (1)

The One-Sample Proportion Test is used to assess whether a population proportion $\hat p$ is significantly different from a hypothesized value $p_o$ .

Calculate the statistic

Since we have all the info requires we can replace in formula (1) like this:

$z=\frac{0.659 -0.5}{\sqrt{\frac{0.5(1-0.5)}{502}}}=7.124$

Statistical decision

It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.

The significance level provided $\alpha=0.01$ . The next step would be calculate the p value for this test.

Since is a right tailed test the p value would be:

$p_v =P(z>7.124)=5.24x10^{-13}$

So the p value obtained was a very low value and using the significance level given $\alpha=0.05$ we have $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 5% of significance the proportion of interest is significantly higher than 0.5.

4 0

3 years ago

One eight of Tony's books are mystery books. He has 3 mystery books. How many books does tony have in all?

Leviafan [203]

Tony has 24 books in total because if 1/8 of the books are mystery and there are 8 mystery books you have to multiple the denominator by the amount of mystery books (8*3=24).

8 0

3 years ago