Question

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? ​

Answer 1

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

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 =
`(X-\mu)/(\sigma)` ~ N(0,1)

where,
`\mu` = population mean number of days = 20 days

`\sigma` = standard deviation = 2 days

So, X ~ Normal(
`\mu=20, \sigma^(2) = 2^(2)`)

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(
`(X-\mu)/(\sigma)` >
`(23-20)/(2)` ) = P(Z > 1.50) = 1 - P(Z
`\leq` 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.