Question

Historically, 92% of the overnight deliveries of a parcel service arrive the next morning before noon (considered “on time” delivery). Suppose 300 deliveries are randomly selected for the purposes of quality control. a. What is the probability that more than 90% of the deliveries were on time? b. What is the probability that less than 85% of the deliveries were on time?

Answer 1

given that p = 0.92

n = 300

mean = p = 0.92

standard error = SE =

(A) P(p> 0.90)

using normalcdf

setting lower = 0.90, upper = 999, mean = 0.92 and se = 0.0157

=normalcdf(lower, upper, mean, se)

=normalcdf(0.90,999,0.92,0.0157)

= 0.8986

(b) P(p< 0.85)

using normalcdf

setting lower = -999, upper = 0.85, mean = 0.92 and se = 0.0157

=normalcdf(lower, upper, mean, se)

=normalcdf(-999,0.85,0.92,0.0157)

= 0.000