Question

A safety light is designed so that the times between flashes are normally distributed with a mean of 4.50 s4.50 s and a standard deviation of 0.50 s0.50 s.

a. Find the probability that an individual time is greater than 5.005.00 s.

b. Find the probability that the mean for 6060 randomly selected times is greater than 5.00 s.5.00 s.

c. Given that the light is intended to help people see an​ obstruction, which result is more relevant for assessing the safety of the​ light?

a. The probability is approximately

​(Round to four decimal places as​ needed.)

Answer 1

a) µ =    4.5                  
σ =    0.5                  
                      
P ( X ≥   5   ) = P( (X-µ)/σ ≥ (5-4.5) / 0.5)              
= P(Z ≥   1.00   ) = P( Z <   -1.000   ) =    0.1587   (answer)

b)

µ =    4.5                                      
σ =    0.5                                      
n=   60                                      
                                          
X =   5                                      
                                          
Z =   (X - µ )/(σ/√n) = (   5   -   4.5   ) / (    0.5   / √   60   ) =   7.746  
                                          
P(X ≥   5   ) = P(Z ≥   7.75   ) =   P ( Z <   -7.746   ) =    0.0000           (answer)

c)  Part (b) is more significant because the average time for a sample is important.