Answer:
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.