Describe the Distribution of the Sample Mean-Samples from a Population That Is Not Normal
-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 $\$ 7000$ ?
A) $0.1814$
B) $0.8186$
C) $0.5675$
D) $0.4325$

Question

Quizplus · Accepted Answer

The distribution of the sample mean will be approximately normal, even if the population distribution is not normal, according to the Central Limit Theorem. The mean of the sample mean will be the same as the mean of the population, which is $7200. The standard deviation of the sample mean will be 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 distribution curve to the right of $7000. This area can be calculated using a standard normal distribution table or a calculator. The z-score for $7000 is (7000 - 7200) / 219.09 = -0.91. The area to the right of -0.91 is 0.1814.Therefore, the probability that the mean daily revenue for the next 30 days will exceed $7000 is 0.1814.

Describe the Distribution of the Sample Mean-Samples from a Population $7200\$ 7200$7200

Describe the Distribution of the Sample Mean-Samples from a Population $\$ 7200$