Question

The resting heart rate for healthy adult horses are normally distributed with an average of

46 beats per minute with a standard deviation of 8 beats per minute. A horse whose resting heart rate is in the upper 10% of the distribution of heart rates may have a secondary infection or illness that needs to be treated. How fast must a healthy horse’sheart be beating to fall into this at-risk group?

Answer 1

Solution:-

Given that,

mean = $\mu$ = 46

standard deviation = $\sigma$ = 8

Using standard normal table,

P(Z > z) = 10%

= 1 - P(Z < z) = 0.10  

= P(Z < z) = 1 - 0.10

= P(Z < z ) = 0.90

= P(Z < 1.28 ) = 0.90  

z = 1.28

Using z-score formula,

x = z * $\sigma$ + $\mu$

x = 1.28 * 8 + 46

x = 56.24