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Let x be a continuous random variable that follows a normal distribution with a mean of 450 and a standard deviation of 80.Find the value of x so that the area under the normal curve between pand x is approximately 0.4591 and the value of x is greater than the mean? Round your answer to the nearest integer.

Let x be a continuous random variable that follows a normal distribution with a mean of 450 and a standard deviation of 80Find the value of x so that the area u class=

Respuesta :

In order to calculate the value of x, first we need to find the value of z such as the area between the mean and x is 0.4591.

Looking at the z-table, the value of z that gives this area is z = 1.74

Then, using the formula for z, we can calculate the value of x:

[tex]\begin{gathered} z=\frac{x-\mu}{\sigma} \\ 1.74=\frac{x-450}{80} \\ x-450=139.2 \\ x=589.2 \end{gathered}[/tex]

Rounding to the nearest integer, we have x = 589.

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