0.4032.
what proportion of temperatures are between 18°C and 20.6°C?
The z-score of the higher given number (20.6);
z-score, z = (x – μ)/ σ
Where,
x is 20.6,
μ is 20.6, and
σ = 2
z = (20.6-20.6) / 2
=0/2
= 0
0 on a z score table is 0.5000.
The z-score of the lower given number (18)
μ is still 20.6 and σ is still 2
z = 18-20.6 /2
= -2.6/2
= -1.3
-1.3 on a z-score table is 0.0968
Hence, subtract our two z-scores
0.5000 - 0.0968 = 0.4032
Therefore, the proportion between 18°C and 20.6°C is 0.4032.
Complete question:
A set of average city temperatures in october are normally distributed with a mean of 20.6°C and a standard deviation of 2°C. what proportion of temperatures are between 18°C and 20.6°C?