Question

A variable is normally distributed with mean 6 and standard 2 deviation .

Answer 1

The normal distribution is also known as the Gaussian distribution. The percentage of all possible values of the variable that are less than 4 is 15.87%.

What is a normal distribution?

The normal distribution, also known as the Gaussian distribution, is a symmetric probability distribution about the mean, indicating that data near the mean occur more frequently than data distant from the mean. The normal distribution will show as a bell curve on a graph.

A.) The percentage of all possible values of the variable that lie between 5 and 9.

P(5<X<9) = P(X<9) - P(5<X)

               = P(z<1.5) - P(-0.5<z)

               = 0.9332 - 0.3085

               = 0.6247

               = 62.47%

B.) The percentage of all possible values of the variable that exceed 1.

P(X>1) = 1 - P(X<-2.5)

          = 1-0.0062

          = 0.9938

          = 99.38%

C.) The percentage of all possible values of the variable that are less than 4.

P(X<4) = P(X <4)

           = P(z<-1)
           = 0.1587

           = 15.87%

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