Question

A simulation study that the transmission delay (measured in milliseconds) of a wireless device connected to RSVP has an approximate normal distribution with an average of 48.5 milliseconds and a standard deviation of 8.5 milliseconds. Present their respective graph.

a. What is the probability that the transmission delay is less than 57 milliseconds? Graph.

b. What is the probability that the transmission delay is 40 and 60 milliseconds?

Answer 1

Solution :

Given that ,

mean = = 48.5

standard deviation = = 8.5

a)

P(x < 57) = P((x - ) / < (57 - 48.5) / 8.5)

= P(z < 1)

= 0.8413 Using standard normal table,

Probability = 0.8413

b)

P(40 < x < 60) = P((40 - 48.5)/ 8.5) < (x - ) /  < (60 - 48.5) / 8.5) )

= P(-1 < z < 1.35)

= P(z < 1.35) - P(z < -1)

= 0.9115 - 0.1587 Using standard normal table,  

Probability = 0.7528