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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? ​

User Vivek
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6 votes

Answer:

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.

User Forivall
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