Question

1. According to the Merck Veterinary Manual, the resting heart rate for an adult horse is about µ = 46 beats per minute with σ = 12 beats per minute. Let x be a random variable that represents the resting heart rate for an adult horse. Consider x to have a distribution that follows a normal distribution. Answer the following questions. Recall the process to derive an answer for finding probabilities and show each step of your work for tractability purposes.

1. What is the probability of finding a heart rate less than 25 beats per minutes?
2. What is the probability of finding a heart rate greater than 65?
3. What is the probability of finding a heart rate between 25 and 65?
4. If a resting horse had a heart rate of greater than 65 beats per minutes, what would you suspect is the health of the horse?

Answer 1

µ = 46

σ = 12

a. P(X < 25)

P(z < -1.750) = 1- P(z < 1.750) = 1- 0.9599 = 0.0401

P(X < 25) = 0.0401

b.P(X >65)

P(z > 1.583) = 1- P(z < 1.583) = 1- 0.9429 = 0.0571

P(X >65) = 0.0571

c. P (25 < X < 65)

P( -1.750 < x < 1.583) = 1- P(z < -1.750) - P(z > 1.583)

P( -1.750 < x < 1.583) = 0.9028

P (25 < X < 65) = 0.9028

d. If a resting horse has a heartrate greater than 65 (the probability is very low 0.0571) which indicates that his health is not normal. He might suffering from some heart problem.