MATH SOLVE

6 months ago

Q:
# Suppose that the distribution of heart rates for medium sized dogs is normally distributed with mean 115 beats per minute and standard deviation 18 beats per minute. Stacy takes her medium sized dog, Scooter to the veterinarian for a wellness check and learns that scooters heart rate is 126 beats per minute. Answer question Ca. What is the standard score for scooters heart rate?= .61b.What percentage of medium-sized dogs have a heart rate that is lower than Scooters? = 76%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?

Accepted Solution

A:

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.