Exploring Centripetal Acceleration and Z-Score in Astronaut Training
The Speed of Astronauts in High Centripetal Acceleration Device
Astronauts often undergo special training in which they are subjected to extremely high centripetal accelerations. One device has a radius of 15 m and can accelerate a person at 98 m/s2. What is the speed of the astronaut in this device?
To calculate the speed of the astronaut in the high centripetal acceleration device, we can use the formula:
v = √(r * a)
where:
v = speed of the astronaut
r = radius of the device (15 m)
a = centripetal acceleration (98 m/s2)
Plugging in the values into the formula, we have:
v = √(15 * 98)
v = √1470
v ≈ 38.31 m/s
Therefore, the speed of the astronaut in this high centripetal acceleration device is approximately 38.31 m/s.
Understanding Z-Score in Statistics
A set of data has a mean of 12 and a standard deviation of 3. A data point of the set has a z-score of 1.3. What does a z-score of 1.3 mean?
A z-score measures how many standard deviations a data point is from the mean of the data set. In this case, the z-score is 1.3, which means the data point is 1.3 standard deviations away from the mean.
Given that the mean is 12 and the z-score of the data point is 1.3, we can calculate the actual value of the data point by using the formula:
x = (z * σ) + μ
where:
x = actual value of the data point
z = z-score (1.3)
σ = standard deviation (3)
μ = mean (12)
Plugging in the values into the formula, we get:
x = (1.3 * 3) + 12
x = 3.9 + 12
x = 15.9
Therefore, a z-score of 1.3 means that the data point is 1.3 standard deviations away from the mean of 12, with an actual value of 15.9.
A data point of the set has a z-score of 1.3. What does a z-score of 1.3 mean?
The data point is 1.3 standard deviations away from 12.