a set of average city temperatures in december are normally distributed - A set of average city temperatures in April are normally distributed with a mean of 19.7^\circ C and a standard deviation of 2^\circ C. The average temperature of Kabul is 15^\circ C. What proportion of average city temperature are lower than that of Kabul? You may round your answer to four decimal places.

Sangeetha Pulapaka (last edited 2 years ago) (Expert, Educator @Qalaxia)

The average temperature of Kabul is given as 15^\circ C. The population of average city temperature lower than that of Kabul is

15 - 19.7 = -4.7 relative to the mean.

This is -\frac{4.7}{2} = -2.35 standard deviations relative to the mean.

This is Kabul's average temperature z-score.

We want to find the proportion of average city temperature below -2.35.

So, 0.0094 proportion of average city temperatures are lower than that of Kabul.