Question

A​ city's mean minimum daily temperature in February is 26 degrees F.

Suppose the standard deviation of the minimum temperature in February is 4 degrees F

and that the distribution of minimum temperatures in February is approximately Normal. What percentage of days in February has minimum temperatures below freezing?____________%

​(Round to the nearest integer as​ needed.)

Answer 1

Solution :

Let X be a random variable which represents the minimum daily temperature in February for a city.

Given that,

Mean (μ) = 26 °F

Standard deviation (σ) = 4 °F

We know that, freezing temperature = 32 °F

Hence, we have to obtain P(X < 32 °F).

We know that if X ~ N(μ, σ²) then

​​​​​​

Using "pnorm" function of R we get, P(Z < 1.5) = 0.9332

0.9332 = 93.32%

On rounding to nearest integer we get, 93%.

Hence, 93% of days in February has minimum temperatures below freezing.