Suppose that normal human body temperatures are normally distributed with a mean of 37°c and a standard deviation of 0.2°c what percent of humans have a temperature between 36.6°c and 37.4°c? which normal curve is shaded correctly for this problem

Notice that 36.6 = 37 - 2*0.2 and 37.4 = 37 + 2*0.2, so the range of temperatures 36.6 to 37.4 fall within 2 standard deviations of the mean. The empirical rule says the approximate percentage of humans with body temperatures in this range is 95%.

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:

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.  

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