mean µ = 39 and standard deviation s = 10. Find the following probabilities. (Round your answers to four decimal places.)

Question

(a) x is less than 60

(b) x is greater than 16

(c) x is between 16 and 60

(d) x is more than 60

Answer 1

You need to compute the z-score for each of these and look up the probabilities in a Z table.  The formula for the z-score is 

 

z = (x - mean) / (standard deviation)  

 

(a) z(60) = (60 - 39) / 10 = 2.1, P(Z < 2.1) = 0.9821  

 

(b) is similar but note that P(Z > z) = 1 - P(Z < z) 

 

(c) Note that P(16<x<60) = P(x<60) - P(x<16) 

 

(d) Use the result from (a) and the formula in (b)