Question

A set of average city temperatures in July are normally distributed

with a mean of 23.5 degrees Celsius and a standard deviation of 2 degrees
Celsius. The average temperature of the City of Van Nuys is 23 degrees
Celsius.
What percentage of average city temperatures are higher than that of the
City of Van Nuys?
a) 59.87%
b) 44.04%
C) 55.96%
d) 40.13%

Answer 1

a) 59.87%

Explanation:

Given that the mean temperature (μ) = 23.5°C and the standard deviation (σ) is 2 °C.

The z score is used in statistics to measure number of standard deviation by which the raw score is above or below the mean value, It is calculated using the equation:

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

The average temperature of the City of Van Nuys is 23 degrees. The z score is

`z=(x-\mu)/(\sigma)=(23-23,5)/(2) =-0.25`

P(x > 23) = P(z > -0.25) = 1 - P(z < -0.25) = 1 - 0.4013 = 0.5987 = 59.87%