# Normal Probability and Confidence Interval

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?

#### Solution Summary

The solution provides step by step method for the calculation of normal probability and confidence interval for population mean. Formula for the calculation and Interpretations of the results are also included.