Answer to Question #260361 in Statistics and Probability for Ading

Question

In a city, it is estimated that the maximum temperature in June is normally distributed with a mean of 28º and a standard deviation of 5.4°. Calculate the number of days in this month in which it is expected to reach a maximum of between 22° and 31°.

Answer 1

$\mu=28 \\ \sigma=5.4 \\ P(22<X<31) = P(X<31) -P(X<22) \\ =P(Z< \frac{31-28}{5.4}) -P(Z< \frac{22-28}{5.4}) \\ = P(Z< 0.556) -P(Z< -1.111) \\ = 0.71074 -0.13326 \\ = 0.57748$

There are 30 days in the month of June.

Expected number of days in this month in which it is expected to reach a maximum of between 22° and 31° $= 30 \times 0.5775 = 17.32$

Answer: 17 days