Question

The owner of a computer repair shop has determined that their daily revenue has mean $7200 and standard deviation $1200. The daily revenue totals for the next 30 days will be monitored. What is the probability that the mean daily revenue for the next 30 days will exceed $7500?

Answer #1

TOPIC:Application of the Central limit theorem to find the required probability.

The owner of a computer repair shop has determined that their
daily revenue has mean $7200 and standard deviation $1200. The
daily revenue totals for the next 30 days will be monitored. What
is the probability that the mean daily revenue for the next 30 days
will be between $7000 and $7500? Round to four decimal
places.

The owner of a computer repair shop has determined that their
daily revenue has mean $7200 and standard deviation $1200. The
daily revenue is normally distributed. a) What is the probability
that a randomly selected day will have a revenue of at most $7000?
b) The daily revenue for the next 30 days will be monitored. What
is the probability that the mean daily revenue for the next 30 days
will exceed $7500?

The government of Egypt has determined that the daily tonnage of
shipped goods passing through the Suez Canal follows a distribution
with a mean of 100,000 tons and a standard deviation of 4,000 tons.
The canal is monitored for the next 64 days and the tonnage passing
through on each of these days is recorded. The sample mean and
sample variance of these 64 measurements are then calculated.
Find the value of tonnage for which the probability of the
sample...

. An automotive repair shop has determined that the average
service time on an automobile is 2 hours with a standard deviation
of 32 minutes. A random sample of 64 services is selected.
a.
What is the probability that the sample of 64 will have a mean
service time greater than 114 minutes?
b.
Assume the population consists of 400 services. Determine the
standard error of the mean.

A computer repair shop has two work centers. The first center
examines the computer to see what is wrong, and the second center
repairs the computer. Let x1 and x2 be random variables
representing the lengths of time in minutes to examine a computer
(x1) and to repair a computer (x2). Assume x1 and x2 are
independent random variables. Long-term history has shown the
following times. Examine computer, x1: μ1 = 31.0 minutes; σ1 = 8.8
minutes Repair computer, x2:...

The probability model below describes the number of repair calls
that an appliance repair shop may receive during an hour.
Repair Calls 0 1 2 3
Probability 0.2 0.3 0.4 0.1
On average, the shop receives 1.4 calls an hour, with a
standard deviation of 0.92 calls. Suppose that the appliance shop
plans a 7-hour day.
a) Find the mean and standard deviation of the number of repair
calls they should expect in a day.
The mean number of repair...

It has been determined that the mean amount of time that
computer science majors spend on homework each week is
approximately normally distributed with a mean of 15.2 hours and
standard deviation 3.1 hours. What is the probability that a
randomly selected computer science major will spend more than 14.5
hours on homework in a given week?

The owner of a fish market has an assistant who has determined
that the weights of catfish are normally distributed with a mean of
3.2 pounds and a standard deviation of .8 pounds. What is the
probability that a sample of 64 fish will have a sample mean
between 2.9 and 3.4 pounds?

A large electronics repair shop uses an average of 85 capacitors
a day. The standard deviation is 5 units per day. The buyer follows
this rule: Order when the amount on hand and on order drops to 625
units. Orders are delivered approximately six days after being
placed. The delivery time is Normal with a mean of six days and a
standard deviation of 1.10 days. What is the probability that the
inventory of capacitors will be exhausted before the...

The owner of a fish market has an assistant who has determined
that the weights of catfish are normally distributed, with a mean
of 3.2 pounds and a standard deviation of 0.8 pound. If a sample of
64 fish yields a mean of 3.4 pounds, what is probability of
obtaining a sample mean this large or larger?
0.4987
0.0013
0.0001
0.0228

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