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%

is there a picture

step-by-step explanation:

an

y = 6x -3y -12

y +3y +12 = 6x

=> . x = { 2y / 3 +2 } this is equation of line in terms of x

=> . if line meets the x-axis the co-ordinates of meeting point would be ( x , 0 )

=> . x = 2 ( 0 ) / 3 + 2

=> . x = 2

so, the point is ( 2 , 0 )