Answer:
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%
