## A random variable is normally distributed with a mean of 25 and a standard deviation of 5. If an observation is randomly selected from the d

Question

A random variable is normally distributed with a mean of 25 and a standard deviation of 5. If an observation is randomly selected from the distribution, what value will be exceeded 85% of the time

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6 days 2021-09-13T23:59:43+00:00 1 Answer 0

Value of 26.93 will be exceeded 85% of the time.

Step-by-step explanation:

We are given that a random variable is normally distributed with a mean of 25 and a standard deviation of 5.

Let X = a random variable

So, X ~ N( )

The z score probability distribution is given by;

Z = ~ N(0,1)

where, = population mean = standard deviation

Now, we have to find that value which will be exceeded 85% of the time, i.e.;

P(X > ) = 0.85

1 – P(X ) = 0.85

P(X ) = 0.15

P(  ) = 0.15

P(Z ) = 0.15

Now, in the z table the critical value of whose less than area is 0.15 is given as 0.3853, i.e; = 0.3853  = 25 + 1.9265 = 26.93

Therefore, value of 26.93 will be exceeded 85% of the time.