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?
Accepted Solution
A:
Answer: 0.6915Step-by-step explanation:Given : [tex]\text{Mean}=\mu=10^{\circ}C[/tex][tex]\text{Standard deviation}=\sigma=10^{\circ}C[/tex]Since , the distribution follows a Normal distribution.The formula to calculate the z-score is given by :-[tex]z=\dfrac{x-\mu}{\sigma}[/tex]For x=[tex]15^{\circ}C[/tex][tex]z=\dfrac{15-10}{10}=0.5[/tex]The p-value = [tex]P(z\leq0.5)=0.6914625\approx0.6915[/tex]Hence, the required probability : 0.6915