Question

A city temperature is modeled as a normal random variable with mean and standard deviation both equal to 10 degrees Celsius. What is the probability that the temperature at a randomly chosen time will be less or equal to 15 degrees Celsius?

Answer 1

Answer: 0.6915

Step-by-step explanation:

Given : $\text{Mean}=\mu=10^{\circ}C$

$\text{Standard deviation}=\sigma=10^{\circ}C$

Since , the distribution follows a Normal distribution.

The formula to calculate the z-score is given by :-

$z=\dfrac{x-\mu}{\sigma}$

For x=$15^{\circ}C$

$z=\dfrac{15-10}{10}=0.5$

The p-value = $P(z\leq0.5)=0.6914625\approx0.6915$

Hence, the required probability : 0.6915