Question

Suppose you are working with a data set that is normally distributed, with a mean of 350 and a standard deviation of 47. Determine the value of x from the following information. (Round your answers and z values to 2 decimal places.)

(a) 80% of the values are greater than x. Entry field with incorrect answer (b) x is less than 16% of the values. Entry field with incorrect answer (c) 21% of the values are less than x. Entry field with incorrect answer (d) x is greater than 60% of the values.

Answer 1

Here, we are given the distribution as:

a) The value of x here is computed as:

P(X > x) = 0.8

Converting this to a standard normal variable, we get:

P(Z > -0.8416 ) = 0.8

Therefore, we have here:

Therefore x = 310.4448 is the required value here.

b) Here, we need to find x such that:

P( X > x ) = 0.16

From standard normal variable, we get:

P(Z > 0.9945 ) = 0.16

Therefore, the value of x here is computed as:

c) The value of x here is computed by using the fact that:

P( X < x) = 0.21

From standard normal tables, we have:

P(Z < -0.8064 ) = 0.21

Therefore, the value of x is obtained as:

d) We have here:

P(X < x) = 0.6

From standard normal tables, we have:

P(Z < 0.2533 ) = 0.6

Therefore, the value of x is computed to be: