Question

(2 pts) In a certain age group, the resting pulse rates of adults are known to have a mean of 81 beats per minute (bpm) with a standard deviation of 12 bpm. (a) According to Chebyshev's rule, at least 8/9 proportion of values in the distribution will be between these two bounds: Lower-bound =__________ bpm and upper-bound =_________ bpm. (b) According to Chebyshev's rule, at least 75% of values in the distribution will be between these two bounds: Lower-bound =__________ bpm and upper-bound =______________ bpm. (c) According to Chebyshev's rule, at least 84% of values in the distribution will be between these two bounds: Lower-bound = __________bpm and upper-bound =_________ bpm.

Answer 1

mean = 81
sd = 12
(a)

According to Chebyshev's rule, at least 1−1/k2 of the data lie within k standard deviations of the mean. where k is any positive whole number that is greater than 1. That is at least 8/9 of the data lie within three standard deviations of the mean.
According to Chebyshev's rule, at least 8/9 proportion of values in the distribution will be between these two bounds: Lower-bound =_____81-3*12__= 45___ bpm and upper-bound =____81+3*12 = __117___ bpm.

(b)

According to Chebyshev's rule, a minimum of just 75% of values must lie within two standard deviations of the mean.

According to Chebyshev's rule, at least 75% of values in the distribution will be between these two bounds: Lower-bound =_____81-2*12 = __57___ bpm and upper-bound =_______81+2*12 = 105_______ bpm.

(c)

According to Chebyshev's rule, 89% of values must lie within three standard deviations.

According to Chebyshev's rule, at least 84% of values in the distribution will be between these two bounds: Lower-bound = ____81-3*12__= 45______bpm and upper-bound =_____81+3*12 = __117____ bpm.