Question: Answer parts a, b, and c below.

1. Fill in the blanks to make true statements. A random sample of 150 customers leaving a shopping mall revealed that the mean amount spent was $9.27 with a sample standard deviation of $1.29. Assuming the finite correction factor does not need to be applied, then the standard error of the mean is computed to be ___ \(\frac{1.29}{\sqrt{150}}=0.\text{1}0\text{5328}\) ________. If the size of the population, from which the sample was selected, were less than ___ 3000 _______, then the finite correction factor would be applied when finding the standard error of the mean. Although we do not know the shape of the distribution of the amounts spent by all customers leaving this shopping mall, the central limit theorem could be used for the distribution of the sample means for this problem because ______________ the same size is large enough (larger than 30) ____
2. In the United States, about 60% of the defendants are found guilty in criminal trials. (Source: The Book of Risks , by Larry Laudan, John Wiley and Sons). Suppose you are a news reporter following 12 criminal trials in the USA. Can the probability requested in part c of Problem 5 of this quiz be reasonably approximated by using a normal distribution? Yes or no and why or why not? Support your answer with numerical evidence, but do not actually recalculate the probability for part c of Problem 5.
   NO, because n*p = 0.6*12 = 7.2 and n*q = 0.4*12 = 4.8 < 5
3. Using the standard normal distribution, find P(0 < z < 1).

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