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# Normal Probability and Confidence Interval

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1- The EMT industry reports that the average time it takes to respond to an emergency call is 25 minutes. Assume that is time is normally distributed with a sigma of 4 minutes. What percentage of call will be responded to in less than 20 minutes?

2- To qualify for the Police Academy, a candidate must score the top 15% on the core entrance exam. The exam has mean of 200 and a standard deviation of 15. What is the cut-off core, below which a candidate will be eligible for the academy?

3-The average age of a vehicle registered in US is 8 years (96 months). Assume the ages are normally distributed with a standard deviation of 16 months.
If a random sample of 36 vehicles is taken, what is the probability that the mean of their ages is between 91 an 102 months?

4- The Mass Lottery wants to estimate the average amount of money an individual spends on the lottery each month. A sample of 49 people who play the lottery was taken and their mean of the amount spent on the lottery was \$21.00 with a standard deviation of \$7.30.
a) What is the best point estimate of the amount of money the population spends on the lottery each month?
b) Construct a 90% confidence interval of the population mean.

5- The average price of a pound of bacon is \$2.02. The standard deviation of the price of bacon (normally distributed) is \$0.08.
In a random sample of 49 one-pound packages so bacon, what is the probability that the mean of the sample is less than \$2.01?