Assuming the population has a similar shape as the sample with population mean $

Question

Assuming the population has a similar shape as the sample with population mean $510,000 and population standard deviation $145,000; calculate the probability that in a random sample of size 36, the mean of the sample will be greater than $700,000. You may assume a random sample was taken and the sample came from a big population. However, be sure to check the central limit theorem condition of a large sample size before completing this problem using one complete sentence. If this condition is not met, you cannot complete the problem.

Explanation / Answer

here as samplee size is greater then 30 therefore  central limit theorem condition of a large sample is satisfied.

here std error =std deviation/(n)1/2 =145000/(36)1/2 =24166.67

therefore probability that mean of the sample will be greater than $700,000 =P(Xbar>700000)

=P(Z>(700000-510000)/24166.67)=P(Z>7.821)=0.0000

therefore probability of that happening is nearly 0.

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