Answer:
Step-by-step explanation:
An ellipse is the locus of a point such that its distances from two fixed points, called foci, have a sum that is equal to a positive constant.
The equation of an ellipse with a center at the origin and the x axis as the minor axis is given by:
Since the distance of the satellite from the surface of the moon varies from 357 km to 710 km, hence:
b = 357 km + 959 km = 1316 km
a = 710 km + 959 km = 1669 km
Therefore the equation of the ellipse is:
Answer:
a) 68% of the men fall between 169 cm and 183 cm of height.
b) 95% of the men will fall between 162 cm and 190 cm.
c) It is unusual for a man to be more than 197 cm tall.
Step-by-step explanation:
The 68-95-99.5 empirical rule can be used to solve this problem.
This values correspond to the percentage of data that falls within in a band around the mean with two, four and six standard deviations of width.
<em>a) What is the approximate percentage of men between 169 and 183 cm? </em>
To calculate this in an empirical way, we compare the values of this interval with the mean and the standard deviation and can be seen that this interval is one-standard deviation around the mean:
Empirically, for bell-shaped distributions and approximately normal, it can be said that 68% of the men fall between 169 cm and 183 cm of height.
<em>b) Between which 2 heights would 95% of men fall?</em>
This corresponds to ±2 standard deviations off the mean.
95% of the men will fall between 162 cm and 190 cm.
<em>c) Is it unusual for a man to be more than 197 cm tall?</em>
The number of standard deviations of distance from the mean is
The percentage that lies outside 3 sigmas is 0.5%, so only 0.25% is expected to be 197 cm.
It can be said that is unusual for a man to be more than 197 cm tall.