Answer:
The correct answer is 2.912 cm.
Step-by-step explanation:
A company is designing a new cylindrical water bottle.
Volume of a cylinder is given by π × × h, where h is the height of the cylinder and r is the radius of the cylinder.
The volume of each bottle will be 211 .
The height (h) of the water bottle be 7.9 cm.
Let the radius of the bottle be r cm.
∴ π × × h = 211 ; (π = 3.15)
⇒ × 24.885 = 211
⇒ r = 2.912
The radius of the water bottle is 2.912 cm.
Answer:
Proportion of all bearings falls in the acceptable range = 0.9973 or 99.73% .
Step-by-step explanation:
We are given that the diameters have a normal distribution with a mean of 1.3 centimeters (cm) and a standard deviation of 0.01 cm i.e.;
Mean, = 1.3 cm and Standard deviation,
= 0.01 cm
Also, since distribution is normal;
Z = ~ N(0,1)
Let X = range of diameters
So, P(1.27 < X < 1.33) = P(X < 1.33) - P(X <=1.27)
P(X < 1.33) = P( <
) = P(Z < 3) = 0.99865
P(X <= 1.27) = P( <
) = P(Z < -3) = 1 - P(Z < 3) = 1 - 0.99865
= 0.00135
P(1.27 < X < 1.33) = 0.99865 - 0.00135 = 0.9973 .
Therefore, proportion of all bearings that falls in this acceptable range is 99.73% .