Final answer:
To find the probability that a healthy dog's body temperature falls within a certain range, we can use the properties of the normal distribution. By converting the range to z-scores and finding the corresponding probabilities from the standard normal distribution table or software, we can calculate the probability for the range.
Step-by-step explanation:
To find the probability that a healthy dog's body temperature falls within a certain range, we need to use the properties of the normal distribution. In this case, we have a normally distributed variable with a mean of 107.32°F and a standard deviation of 0.41°F. If we want to find the probability that the dog's body temperature falls within a certain range, we need to calculate the area under the normal curve between the lower and upper limits of that range.
To do this, we can use the standard normal distribution table or a statistical software. We will convert the lower and upper limits of the range to z-scores, which represent the number of standard deviations a value is from the mean. Then, we can use the z-scores to find the corresponding probabilities from the standard normal distribution table or software.
For example, if we want to find the probability that the body temperature is between 106°F and 108°F, we first need to convert these temperatures to z-scores. The z-score formula is z = (x - mean) / standard deviation.
For the lower limit, z = (106 - 107.32) / 0.41 = -3.22. For the upper limit, z = (108 - 107.32) / 0.41 = 1.66. Using the standard normal distribution table or software, we can find the corresponding probabilities for these z-scores. The probability for the range is then the difference between these two probabilities.