A set average city temperatures in August are normally distributed with a mean of 21.25 degrees Celsius and a standard deviation of 2 degrees Celsius. what proportion of temperature are between 23.71 degrees Celsius and 26.17 degrees Celsius .

The proportion of temperatures that lie within the given limits are 10.24%

Step-by-step explanation:

Solution:-

- Let X be a random variable that denotes the average city temperatures in the month of August.

- The random variable X is normally distributed with parameters:

                           mean ( u ) = 21.25

                           standard deviation ( σ ) = 2

- Express the distribution of X:

                           X ~ Norm ( u , σ^2 )

                           X ~ Norm ( 21.25 , 2^2 )

- We are to evaluate the proportion of set of temperatures in the month of august that lies between 23.71 degrees Celsius and 26.17 degrees Celsius :

                           P ( 23.71 < X < 26.17 )

- We will standardize our limits i.e compute the Z-score values:

                          P (  (x1 - u) / σ < Z < (x2 - u) / σ )

                          P (  (23.71 - 21.25) / 2 < Z < (26.17 - 21.25) / 2  )

                          P ( 1.23 < Z < 2.46 ).

- Now use the standard normal distribution tables:

                          P ( 1.23 < Z < 2.46 ) = 0.1024

- The proportion of temperatures that lie within the given limits are 10.24%

sas (side angle side)

aa (angle angle)

sss(side side side)

sas find two sides with an angle in between

aa is finding two angles and the third will add up to 180

sss find all sides

step-by-step explanation: