Question

a set of average city temperatures in december are normally distributed with a mean of 16.3°c and a standard deviation of 2°c. what proportion of temperatures are between 12.9°c and 14.9°c? you may round your answer to four decimal places.

Explanation:

Step1: Calculate z - scores

The formula for the z - score is $z=\frac{x-\mu}{\sigma}$, where $\mu$ is the mean, $\sigma$ is the standard deviation, and $x$ is the value from the data - set.
For $x = 12.9$, $z_1=\frac{12.9 - 16.3}{2}=\frac{- 3.4}{2}=-1.7$.
For $x = 14.9$, $z_2=\frac{14.9 - 16.3}{2}=\frac{-1.4}{2}=-0.7$.

Step2: Use the standard normal distribution table

We want to find $P(-1.7We know that $P(-1.7From the standard - normal distribution table, $P(Z < - 0.7)=0.2420$ and $P(Z < - 1.7)=0.0446$.

Step3: Calculate the probability

$P(-1.7

Answer:

$0.1974$