Answer:
95%.
Step-by-step explanation:
We have been given that the normal human body temperatures are normally distributed with a mean of 37°C and a standard deviation of 0.2°C. We are asked to find the percentage of of humans have a temperature between 36.6°C and 37.4°C.
First of all, we will find z-score corresponding to both values as:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
[tex]z=\frac{36.6^{\circ}C-37^{\circ}C}{0.2^{\circ}C}}[/tex]
[tex]z=\frac{-0.4^{\circ}C}{0.2^{\circ}C}}[/tex]
[tex]z=-2[/tex]
[tex]z=\frac{x-\mu}{\sigma}[/tex]
[tex]z=\frac{37.4^{\circ}C-37^{\circ}C}{0.2^{\circ}C}}[/tex]
[tex]z=\frac{0.4^{\circ}C}{0.2^{\circ}C}}[/tex]
[tex]z=2[/tex]
We can see that both z-scores lies within two standard deviation of the mean.
By empirical rule 68% of data points on normal distribution lies within one standard deviation of the mean.
95% of data points on normal distribution lies within two standard deviations of the mean.
99.7% of data points on normal distribution lies within three standard deviations of the mean.
Therefore, 95% of humans have a temperature between 36.6°C and 37.4°C.
