Question

A set of average city temperatures in May are normally distributed with a mean of 20.66°C and a standard

Answer 1

We have been given that a set of average city temperatures in May are normally distributed with a mean of 20.66°C and a standard  deviation of 2 C. The average temperature of Singapore is 26°C. We are asked to find the proportion of average city temperatures that are lower than that of Singapore.

First of all, we will find z-score corresponding to sample score of 26.

$z=\frac{x-\mu}{\sigma}$, where,

z = z-score,

x = Random sample score,

$\mu$ = Mean,

$\sigma$ = Standard deviation.

$z=\frac{26-20.66}{2}$

$z=\frac{5.34}{2}$

$z=2.67$

Now we need to find probability of a z-score less than 2.67 that is $P(z$.

Using normal distribution table, we will get:

$P(z$

Upon rounding to 4 decimal places, we will get:

$P(z$

Therefore, approximately $0.9962$ of average city temperatures are lower than that of Singapore.