1) Confidence Interval for Mean (5 caselets)
Qt.I - Cafe daily revenue
A cafe tracked its daily revenue for 50 weekdays. The sample mean revenue was t48,000 and
the population standard deviation (based on past data) is known to be t8,000.
Construct a 95•;. confidence interval for the true average weekday revenue of the cafe.
Qt.2 - Manufacturing cycle time
ln a manufacturing plant, the cycle time (in minutes) for a particular machine was recorded for
a random sample of 36 cycles. The sample mean was 15.5 minutes. Assume the population
standard deviation is known to be 3 minutes (based on historical data).
Construct a 99•;. confidence interval for the true mean cycle time.
Qt.3 - Monthly electricity bill of a small office
For a small office, the past 40 months' electricity bills were analyzed. The sample mean
monthly bill was t9,600 and the population standard deviation is known to be tl,500.
Construct a 90•;. confidence interval for the true mean monthly electricity bill.
Qt.4-Average time spent on an app
A marketing team measures the time (in minutes) users spend per session on their app. A large
random sample of 100 sessions shows a sample mean of 18 minutes, with a population
standard
deviation
of
4.5
minutes
(assumed
known).
Construct a 95•;. confidence interval for the true mean session time.
Qt.5 - Call centre handling t.ime
1n a call centre, it is known from historical records that the standard deviation of call bandl ing
time is 2.5 minutes. A sample of 64 calls this month has an average handling time of 6.8
minutes.
Construct a 981/o confidence interval for the true mean call handling time.
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