Respuesta :
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.
[tex]z=\frac{x-\mu}{\sigma}[/tex], where,
z = z-score,
x = Random sample score,
[tex]\mu[/tex] = Mean,
[tex]\sigma[/tex] = Standard deviation.
[tex]z=\frac{26-20.66}{2}[/tex]
[tex]z=\frac{5.34}{2}[/tex]
[tex]z=2.67[/tex]
Now we need to find probability of a z-score less than 2.67 that is [tex]P(z<2.67)[/tex].
Using normal distribution table, we will get:
[tex]P(z<2.67)=0.99621[/tex]
Upon rounding to 4 decimal places, we will get:
[tex]P(z<2.67)\approx 0.9962[/tex]
Therefore, approximately [tex]0.9962[/tex] of average city temperatures are lower than that of Singapore.
