The mean number of days to observe rain in a particular city is 20 days with a standard deviation of 2 days. Suppose that the rain pattern is Normally distributed. what is the probability of raining if the number of days are more than 23?

The probability of raining if the number of days is more than 23 is 0.0668.

Step-by-step explanation:

We are given that the mean number of days to observe rain in a particular city is 20 days with a standard deviation of 2 days.

Let X = Number of days of observing rain in a particular city.

The z-score probability distribution for the normal distribution is given by;

                         Z  =    ~ N(0,1)

where, = population mean number of days = 20 days

            = standard deviation = 2 days

So, X ~ Normal()

Now, the probability of raining if the number of days is more than 23 is given by = P(X > 23 days)

        P(X > 23 days) = P( > ) = P(Z > 1.50) = 1 - P(Z 1.50)

                                                              = 1 - 0.9332 = 0.0668

The above probability is calculated by looking at the value of x = 1.50 in the z table which has an area of 0.9332.