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%