1- Suppose that the distribution for total amounts spent by students vacationing for a week in Florida is normally distributed with a mean of 650 and a standard deviation of 120. Suppose you take a simple random sample (SRS) of 45 students from this distribution.

What is the probability that a SRS of 45 students will spend an average of between 600 and 700 dollars?

Round to five decimal places

2- A factory produces plate glass with a mean thickness of 4mm and a standard deviation of 1.1mm. A simple random sample of 100 sheets of glass is to be measured, and the mean thickness of the 100 sheets is to be computed.

What is the probability that the average thickness of the 100 sheets is less than 4.13 mm?

Round to five decimal places

3- A machine is designed to fill 16-ounce bottles of shampoo. When the machine is working properly, the amount poured into the bottles follows a normal distribution with mean 16.05 ounces with a standard deviation of .4 ounces.

If four bottles are randomly selected each hour and the number of ounces in each bottle is measured, then 95% of the means calculated should occur in what interval?

Hint: the standard deviation rule says that 95% of the observations are within how many standard deviations away from the mean?

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Round answers to four decimal places.