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

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=(x-\mu)/(\sigma)`

For x=
`15^(\circ)C`

`z=(15-10)/(10)=0.5`

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

Hence, the required probability : 0.6915