The owner of a computer repair shop has determined that their daily revenue has mean $7200 and standarddeviation $1200. The daily revenue totals for the next 30 days will be monitored. What is the probability thatthe mean daily revenue for the next 30 days will exceed $7000?
A) 0.1814
B) 0.8186
C) 0.5675
D) 0.4325

Question

Quizplus · Accepted Answer

The central limit theorem states that the distribution of sample means will be approximately normal, regardless of the shape of the population distribution, if the sample size is large enough. In this case, the sample size is 30, which is large enough to apply the central limit theorem.The mean of the sample means will be equal to the mean of the population, which is $7200. The standard deviation of the sample means will be equal to the standard deviation of the population divided by the square root of the sample size, which is $1200 / sqrt(30) = $219.09.The probability that the mean daily revenue for the next 30 days will exceed $7000 is the area under the normal curve to the right of $7000. This area can be calculated using a standard normal distribution table or a calculator. The area to the right of $7000 is 0.1814.Therefore, the correct answer is A) 0.1814.

The Owner of a Computer Repair Shop Has Determined That