Answer:
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Step-by-step explanation:
I'm pretty sure this is the answer.
What number is 80% of 390?
2 answers:
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Answer:
(a) The probability that the thickness is less than 3.0 mm is 0.119.
(b) The probability that the thickness is more than 7.0 mm is 0.119.
(c) The probability that the thickness is between 3.0 mm and 7.0 mm is 0.762.
Step-by-step explanation:
We are given that thickness measurements of ancient prehistoric Native American pot shards discovered in a Hopi village are approximately normally distributed, with a mean of 5.0 millimeters (mm) and a standard deviation of 1.7 mm.
Let X = <u><em>thickness measurements of ancient prehistoric Native American pot shards discovered in a Hopi village.</em></u>
So, X ~ Normal()
The z-score probability distribution for the normal distribution is given by;
Z = ~ N(0,1)
where, = population mean thickness = 5.0 mm
= standard deviation = 1.7 mm
(a) The probability that the thickness is less than 3.0 mm is given by = P(X < 3.0 mm)
P(X < 3.0 mm) = P( <
) = P(Z < -1.18) = 1 - P(Z
1.18)
= 1 - 0.8810 = <u>0.119</u>
The above probability is calculated by looking at the value of x = 1.18 in the z table which has an area of 0.881.
(b) The probability that the thickness is more than 7.0 mm is given by = P(X > 7.0 mm)
P(X > 7.0 mm) = P( >
) = P(Z > 1.18) = 1 - P(Z
1.18)
= 1 - 0.8810 = <u>0.119</u>
The above probability is calculated by looking at the value of x = 1.18 in the z table which has an area of 0.881.
(c) The probability that the thickness is between 3.0 mm and 7.0 mm is given by = P(3.0 mm < X < 7.0 mm) = P(X < 7.0 mm) - P(X 3.0 mm)
P(X < 7.0 mm) = P( <
) = P(Z < 1.18) = 0.881
P(X 3.0 mm) = P(
) = P(Z
-1.18) = 1 - P(Z < 1.18)
= 1 - 0.8810 = 0.119
The above probability is calculated by looking at the value of x = 1.18 in the z table which has an area of 0.881.
Therefore, P(3.0 mm < X < 7.0 mm) = 0.881 - 0.119 = 0.762.
The pyramid is shown in the diagram below.
The pyramid is built from four congruent triangles and one square as the base
We have the side of the square, so the area is = 10×10 = 100
We need the height of the triangle to work out its area. We can find out by using the height of the pyramid and half of the length of the side of the square.
Using the Pythagoras rule
Height of triangle =
Area of one triangle = 1/2×10×12=60
Surface area of the pyramid = 100 + (4×60) = 340 square inches
The pyramid is built from four congruent triangles and one square as the base
We have the side of the square, so the area is = 10×10 = 100
We need the height of the triangle to work out its area. We can find out by using the height of the pyramid and half of the length of the side of the square.
Using the Pythagoras rule
Height of triangle =
Area of one triangle = 1/2×10×12=60
Surface area of the pyramid = 100 + (4×60) = 340 square inches