Question

A set of average city temperatures in August is normally distributed with a mean of 21.25°C and a standard deviation of 2°C. What proportion of temperatures are between 19.63°C and 20.53°C? You may round your answer to four decimal places.

Answer 1

To find the proportion of temperatures between 19.63°C and 20.53°C, calculate the z-values for each temperature using the mean and standard deviation, then use a standard normal distribution table or calculator to find the proportion between these z-values.

Step-by-step explanation:

To find the proportion of temperatures between 19.63°C and 20.53°C, we need to convert these temperatures to standard units using the formula z = (x - mean) / standard deviation. For 19.63°C, the z-value is (19.63 - 21.25) / 2 = -0.81. For 20.53°C, the z-value is (20.53 - 21.25) / 2 = -0.36. We can then use a standard normal distribution table or calculator to find the proportion of temperatures between these z-values.

Using a standard normal distribution table or calculator, we find that the proportion of temperatures between -0.81 and -0.36 is approximately 0.1645.