Question

A​ city's mean minimum daily temperature in February is 22 degrees Upper F. Suppose the standard deviation of the minimum temperature in February is 6 degrees Upper F and that the distribution of minimum temperatures in February is approximately Normal. What percentage of days in February has minimum temperatures below freezing left parenthesis 32 degrees Upper F right parenthesis​?

Answer 1

Probability that X <32 degrees

`=P(Z<(32-22)/(6)) =P(Z<1.67)\\ = 0.9522`

Convert this into percent by multiplying by 100

95.22% of days in February has minimum temperatures below freezing (32 degrees Upper F )​

Explanation:

Given that a city's mean minimum daily temperature in February is 22 degrees Upper F, with std deviation 6 degrees.

Let X be the minimum temperature in February

Then X is N(22,6)

To calculate percentage of days in February has minimum temperatures below freezing (32 degrees Upper F )

Probability that X <32 degrees

`=P(Z<(32-22)/(6)) =P(Z<1.67)\\ = 0.9522`

Convert this into percent by multiplying by 100

95.22% of days in February has minimum temperatures below freezing (32 degrees Upper F )​