Question

Problem (15 points) VTE telephone operators are assigned to handle all 411 calls. The mean time to respond to a caller is 30 seconds with a standard deviation of 5 seconds (Hint: draw a picture of the normal distribution curve for each problem). Use 4 decimal places of accuracy a) What is the probability that your call will be handled in less than 27 seconds? (2 points) b What proportion of calls are responded to in 23 to 27 seconds? (2 points) c What proportion of calls are responded to in 27 to 33.3 seconds? (2 points) d) What proportion of calls are responded to in about 35 seconds? (2 points)

Answer 1

Solution:- Given that n = 411, mean = 30 , standard deviation = 5

a) P(X < 27) = P((X-μ)/( σ/sqrt(n)) < (27-30)/(5/sqrt(411)))
= P(Z < -12.1638)
= 0

b) P(23 < X < 27) = P((23-30)/(5/sqrt(411)) Z < (27-30)/(5/sqrt(411)))
= P(-28.3823 < Z < -12.1638)
= 0

c) P(27 < X < 33.3) = P((27-30)/(5/sqrt(411) < Z < (33.3-30)/(5/sqrt(411)))
= P(-12.1638 < Z < 13.3802)
= 1

d) P(X > 35) = P(Z > (35-30)/(5/sqrt(411)))
= P(Z > 20.2731)
= 0