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A random sample of n = 9 structural elements is tested for comprehensive strength. We know the true mean comprehensive strength

irinina [24]

Answer:

Probability that the sample mean comprehensive strength exceeds 4985 psi is 0.99999.

Step-by-step explanation:

We are given that a random sample of n = 9 structural elements is tested for comprehensive strength. We know the true mean comprehensive strength μ = 5500 psi and the standard deviation is σ = 100 psi.

Let $\bar X$ = sample mean comprehensive strength

The z-score probability distribution for sample mean is given by;

Z = $\frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n} } }$ ~ N(0,1)

where, $\mu$ = population mean comprehensive strength = 5500 psi

$\sigma$ = standard deviation = 100 psi

The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X.

Now, Probability that the sample mean comprehensive strength exceeds 4985 psi is given by = P( $\bar X$ > 4985 psi)

P( $\bar X$ > 4985 psi) = P( $\frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n} } }$ > $\frac{4985-5500}{\frac{100}{\sqrt{9} } }$ ) = P(Z > -15.45) = P(Z < 15.45)

= 0.99999

Since in the z table the highest critical value of x for which a probability area is given is x = 4.40 which is 0.99999, so we assume that our required probability will be equal to 0.99999.

4 0

4 years ago

to find the perimeter of the rectangle you can see the formula P=21+2W. find the perimeter P of a rectangle whose length L is 10

Olin [163]

Answer:

rectangle, the distance around the outside of the rectangle is known as perimeter. A rectangle is 2-dimensional; however, perimeter is 1-dimensional and is measured in linear units such as feet or meter etc.

The perimeter of a rectangle is the total length of all the four sides.

Perimeter of rectangle = 2L + 2W.

Example 1: Rectangle has the length 13 cm and width 8 cm. solve for perimeter of rectangle.

Solution:

Given that:

Length (l) = 13 cm

Width (w) = 8 cm

Perimeter of the rectangle = 2(l + w) units

P = 2(13 + 8)

P = 2 (21)

P = 42

Thus, the perimeter of the rectangle is 42 cm.

Example 2: If a rectangle's length is 2x + 1 and its width is 2x – 1. If its area is 15 cm2, what are the rectangle's dimensions and what is its perimeter?

Solution:

We know that the dimensions of the rectangle in terms of x:

l = 2x + 1

w = 2x – 1

Since the area of a rectangle is given by:

A = l * w

We can substitute the expressions for length and width into the equation for area in order to determine the value of x.

A = l * w

15 = (2x + 1) (2x -1)

15 = 4x2 – 1

16 = 4x2

x = ±2

Note that the value of x must be positive and therefore in our case, the value of x is 2. And now we have:

l = 5 cm

w = 3 cm

Therefore, the dimensions are 5cm and 3cm.

Now, substituting these values in the formula for perimeter, we will get

P = 2l + 2w

P = 2(5)+2(3)

P = 10+6

P = 16 cm

Example 3: Find the area and the perimeter of a rectangle whose length is 24 m and width is 12m?

Solution:

Given that:

length = L = 24m

width = W = 12m

Area of a rectangle:

A = L × W

A = 24 × 12

A = 188 m2

Perimeter of a rectangle:

P = 2L + 2W

P = 2(24) + 2(12)

P = 48 + 24

P = 72 m

Example 4: Find the area and perimeter of a rectangle whose breadth is 4 cm and the height 3 cm.

Solution:

Area = b×h = 4×3 = 12 cm2.

Perimeter = 2(b) + 2(h) = 2(4) + 2(3) = 8 + 6 = 14.

Example 5: Calculate the perimeter of the rectangle whose length is 18cm and breadth 7cm

Solution:

Given that:

L = 18 cm

B = 7 cm

Perimeter of rectangle = 2(length + breadth)

P = 2 (L + B)

P = 2 (18 + 7)

P = 50 cm

Example 6: Find the perimeter of rectangle whose length is 6 inches and width is 4 inches.

Solution:

P = 2(L + B)

P = 2(6 + 4)

P = 20 in

Example 7: A boy walks 5 times around a park. If the size of the park is 100m by 50m, find the distance the boy has walked. If he walks 100m in 5 minutes, how long will it take for him in total?

Solution:

Given that:

Length = L = 100m

Width = W = 50m

Rounds = 5

Time per 100m = 5minutes.

Perimeter of the park:

P = 2 L + 2 W.

P = 2 × 100 + 2 × 50

P = 200 + 100

P = 300 m

Total distance walked = 5 × Perimeter of the park.

= 5 × 300

= 1500 meters

Total time taken = Total distance walked × time taken to walk 1m.

= 1500 × 5/100

= 75minutes or 1hr 15minutes

6 0

3 years ago

Due Soon Need Help Geometry!

AveGali [126]

Some basic formulas involving triangles

\ a^2 = b^2 + c^2 - 2bc \textrm{ cos } \alphaa 2 =b 2+2 + c 2

−2bc cos α

\ b^2 = a^2 + c^2 - 2ac \textrm{ cos } \betab 2=

m_b^2 = \frac{1}{4}( 2a^2 + 2c^2 - b^2 )m b2 = 41(2a 2 + 2c 2-b 2)

b

Bisector formulas

\ \frac{a}{b} = \frac{m}{n} ba =nm

\ l^2 = ab - mnl 2=ab-mm

A = \frac{1}{2}a\cdot b = \frac{1}{2}c\cdot hA=

\ A = \sqrt{p(p - a)(p - b)(p - c)}A=

p(p−a)(p−b)(p−c)

\iits whatever A = prA=pr with r we denote the radius of the triangle inscribed circle

\ A = \frac{abc}{4R}A=

4R

abc

- R is the radius of the prescribed circle

\ A = \sqrt{p(p - a)(p - b)(p - c)}A=

p(p−a)(p−b)(p−c)

5 0

3 years ago

A piece of stained glass in the shape of a right triangle has sides measuring 8 centimeters 15 centimeters and 16 centimeters wh

Wittaler [7]

The answer would be...

a= 59.43 sq. cm

3 0

3 years ago

Which function has the domain x>or= -11

iogann1982 [59]

I'm assuming this is multiple choice and you forgot to post the answers. I'll take a guess and say it probably looks something like this:
$y = \sqrt{x + 11}$
Because you can't take the square root of a negative number without getting an imaginary result, resulting in the function having a closed domain limit.

6 0

3 years ago