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Andrej [43]
2 years ago
15

Assume that weights of men are normally distributed with a mean of 170 lb and a standard deviation of 30 lb (approximate values

based on data from the National Health and Nutrition Examination Survey). What percentage of individual men have weights less than 185 lb? If samples of 36 men are randomly selected and the mean weight is computed for each sample, what percentage of the sample means are less than 185 lb?
a. 0.3156
b. 0.2611
c. 0.2312
d. 0.4602
Mathematics
1 answer:
Lubov Fominskaja [6]2 years ago
4 0

Answer:

a) P(X

b) P(\bar X

Step-by-step explanation:

1) Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

2) Part a

Let X the random variable that represent the weights of men of a population, and for this case we know the distribution for X is given by:

X \sim N(170,30)  

Where \mu=170 and \sigma=30

We are interested on this probability

P(X

And the best way to solve this problem is using the normal standard distribution and the z score given by:

z=\frac{x-\mu}{\sigma}

If we apply this formula to our probability we got this:

P(X

And we can find this probability on this way:

P(Z

3) Part b

The central limit theorem states that "if we have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed. This will hold true regardless of whether the source population is normal or skewed, provided the sample size is sufficiently large".

From the central limit theorem we know that the distribution for the sample mean \bar X is given by:

\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})

P(\bar X

And using a calculator, excel or the normal standard table we have that:

P(Z

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dusya [7]

Answer:

1. y + 10 - 3/2y = -y/2 + 10

2. 2r+ 7r-r - 9 = 8r - 9

3.  7 + 4p-5+p+2q = 2 + 5p + 2q

Step-by-step explanation:

basically you can add terms that have the same variable

integers can be added together, Xs can be added, Zs, Ys, As, Bs, Cs, you get the point

1. y + 10 - 3/2y = -y/2 + 10

2. 2r+ 7r-r - 9 = 8r - 9

3.  7 + 4p-5+p+2q = 2 + 5p + 2q (do not add different variables p and q ) together

try 4-6 on your own to get this skill down, if you need help with those just let me know

7 0
3 years ago
What is the length of s?​
vovangra [49]

Answer:

s = 16.97 units

Step-by-step explanation:

Since this is a right triangle, we can use trigonometry to figure out the lengths of the sides.

Look at the 45 degree angle. We can use the opposite side (12) and the hypotenuse (s) to solve for s.

Opposite and hypotenuse is sine, so we are using sine. The sine of 45 degrees is 0.70710678118. Make an equation like so:

  • 0.70710678118 = \frac{12}{s}, and we are solving for s.

Put a 1 in the denominator of sine(45 degrees) so you can cross-multiply.

  • \frac{0.70710678118}{1} =\frac{12}{s}

Cross multiply.

  • 0.70710678118s = 12

Divide both sides by sine(45 degrees).

  • s = 16.97

The length of side s is 16.97 units.

Another way to have done this problem is to use the Pythagorean theorem: a^2 + b^2 = c^2

Substitute 12 for a and b and solve for c, the hypotenuse.

  • (12)^2 + (12)^2 = c^2

Evaluate the exponents.

  • 144 + 144 = c^2

Add them together.

  • 288 = c^2

Square root 288 to solve for c.

c = 16.97, which is the same answer as you got using trigonometry.

6 0
3 years ago
What is the length of side BC of the triangle? Enter your answer in the box. units Triangle A B C with horizontal side B C. Vert
harina [27]

Answer:

The length of BC = 28 units

Step-by-step explanation:

* In triangle ABC

∵ Angles B and C are congruent

∴ m∠B = m∠C

* In any triangle if two angles are equal in measure, then the triangle is isosceles means the two sides which opposite to the congruent angles are equal in length

∴ AB = AC

∵ AB = 4x - 7

∵ AC = 2x + 7

∴ 4x - 7 = 2x + 7 ⇒ collect like terms

∴ 4x - 2x = 7 + 7

∴ 2x = 14 ⇒ divide both sides by 2

∴ x = 14 ÷ 2 = 7

* Now we can find the length of BC

∵ The length of BC = 4x ⇒ substitute the value of x

∴ The length of BC = 4 × 7 = 28 units

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Virty [35]

Answer:

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Step-by-step explanation:

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zaharov [31]

Answer:

X-8 is the best answer there

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