Answer :
Answer:
a) The standard score for Scooter's heart rate is 0.61.
b) 72.91% of medium-sized dogs have a heart rate that is lower than Scooters.
c) For medium-sized dogs, a dangerous heart rate would be one above 140.29 beats per minute.
Step-by-step explanation:
Problems of normally distributed samples can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this problem, we have that:
Normally distributed with mean 115 beats per minute and standard deviation 18 beats per minute. This means that [tex]\mu = 115, \sigma = 18[/tex].
a. What is the standard score for scooters heart rate?
Scooter to the veterinarian for a wellness check and learns that scooters heart rate is 126 beats per minute. This means that [tex]X = 126[/tex].
The standard score is his zscore.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{126 - 115}{18}[/tex]
[tex]Z = 0.61[/tex]
The standard score for Scooter's heart rate is 0.61.
b.What percentage of medium-sized dogs have a heart rate that is lower than Scooters?
This percentage is the pvalue of [tex]Z = 0.61[/tex].
[tex]Z = 0.61[/tex] has a pvalue of 0.7291. This means that 72.91% of medium-sized dogs have a heart rate that is lower than Scooters.
c. Stacy learns from the veterinarian that dogs with heart rates in the upper 8% may be in danger of heart failure. For medium-sized dogs, a dangerous heart rate would be one above what value?
This is the value of X when Z has a pvalue of 0.92. This is [tex]Z = 1.405[/tex]. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.405 = \frac{X - 115}{18}[/tex]
[tex]X - 115 = 18*1.405[/tex]
[tex]X = 140.29[/tex]
For medium-sized dogs, a dangerous heart rate would be one above 140.29 beats per minute.