Question

Teleconferences, electronic mail, and word processors are among the tools that can
reduce the length of business meetings. A recent survey indicated that the percentage
reduction y in time spent by business professionals in meetings due to an automated office
equipment is approximately normally distributed with mean equal to 15% and standard
deviation equal to 4%.

a. what proportion of all business professionals with access to automated office equipment
have reduced their time in meetings by more than 22%

a. what proportion of all business professionals with access to automated office equipment
have reduced their time in meetings by 10 % or less?

Answer 1

Let y: time spent by business professionals in meeting due to automated office equipment is approximately normal with mean % and standard deviation %.

a) The proportion of all business professionals with access to automated office equipment have reduced their time in meetings by more than 22% that is P(Y > 22%)

Convert y into z score, the formula of z score is

That is P(Y > 22%) becomes P(Z > 1.75)

The probability for z = 1.75 using standard normal table is 0.9599

but the table provides the less than probability, to find more than just subtract it from 1

1 - 0.9599 = 0.0401

Therefore, the proportion of all business professionals with access to automated office equipment
have reduced their time in meetings by more than 22% is 0.0401

b. The proportion of all business professionals with access to automated office equipment
have reduced their time in meetings by 10 % or less that is

Convert Y = 10% into z score,

becomes

The probability using the standard normal table for z = -1.25 is 0.1057

Therefore, the proportion of all business professionals with access to automated office equipment
have reduced their time in meetings by 10 % or less is 0.1057