Twice a number added to another number is –8. The difference of the two numbers is 2. Find
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Answer:
Probability that the sample mean would be greater than 141.4 millimetres is 0.3594.
Step-by-step explanation:
We are given that Thompson and Thompson is a steel bolts manufacturing company. Their current steel bolts have a mean diameter of 141 millimetres, and a standard deviation of 7.
A random sample of 39 steel bolts is selected.
Let = <u><em>sample mean diameter</em></u>
The z score probability distribution for sample mean is given by;
Z = ~ N(0,1)
where, = population mean diameter = 141 millimetres
= standard deviation = 7 millimetres
n = sample of steel bolts = 39
Now, Percentage the sample mean would be greater than 141.4 millimetres is given by = P( > 141.4 millimetres)
P( > 141.4) = P(
>
) = P(Z > 0.36) = 1 - P(Z
0.36)
= 1 - 0.6406 = <u>0.3594</u>
The above probability is calculated by looking at the value of x = 0.36 in the z table which has an area of 0.6406.
a. Length of the fence around the field = perimeter of quarter circle = 892.7 ft.
b. The area of the outfield is about 39,584 sq. ft..
<h3>What is the Perimeter of a Quarter Circle?</h3>Perimeter of circle = 2πr
Perimeter of a quarter circle = 2r + 1/4(2πr).
a. The length of the fence around the field = perimeter of the quarter circle fence
= 2r + 1/4(2πr).
r = 250 ft
Plug in the value
The length of the fence around the field = 2(250) + 1/4(2 × π × 250)
= 892.7 ft.
b. Size of the outfield = area of the full field (quarter circle) - area of the infield (cicle)
= 1/4(πR²) - πr²
R = radius of the full field = 250 ft
r = radius of the infield = 110/2 = 55 ft
Plug in the values
Size of the outfield = 1/4(π × 250²) - π × 55²
= 49,087 - 9,503
= 39,584 sq. ft.
Learn more about perimeter of quarter circle on:
