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- The Australian Emergency department reports that the average time it takes to respond to an emergency call is 20 minutes. Assume the variable is approximately normally distributed and the standard deviation is 5 minutes. If 80 calls are randomly selected, what is probability a emergency call will be responded between 12 and 25 minutes?A typical adult has an average IQ score of 105 with a standard deviation of 20. If 20 randomly selected adults are given an IQ test, what is the probability that the sample mean is between 85 and 125 points?2. The average number of liters of water that a person consume in a month is 12 liters. Assume that the standard deviation is 4.5 liters and the distribution is approximately normal. a. Find the probability that a person selected at random consumes more than 13 liters per month. b. If a sample of 20 individuals is selected, find the probability that mean of the sample will be more than 13 liters.
- 3. The finish times for marathon runners during a race are normally distributed with a mean of 195 minutes and a standard deviation of 25 minutes. What is the probability that a runner will complete the marathon within 180 minutes?Suppose the heights of a group of people follow a normal distribution with a mean of 170 cm and a standard deviation of 10 cm. If 25% of the people are shorter than 160 cm, what is the minimum height required to be in the tallest 10% of the group? If a sample of 50 people is randomly selected from the group, what is the probability that their average height is between 168 and 172 cm?Suppose the average amount of money that people spend on their pets per month is 47 dollars, with a standard deviation of 6 dollars. For a sample of 36 people, final the average amount of money spent on pets that defines the bottom 30% in the distribution.For a sample of 36 people, what is the probability for this sample’s mean to be higher than 50 dollars.
- 7. Furnace repair bills are normally distributed with a mean of 267 dollars and a standard deviation of 20 dollars. If 74 of these repair bills are randomly selected, find the probability that they have a mean cost between 267 dollars and 269 dollars.8. An HP laser printer is advertised to print text documents at a speed of 18 ppm (pages per minute). The manufacturer tells you that the printing speed is actually a Normal random variable with a mean of 17.57 ppm and a standard deviation of 3 ppm. A Brother brand printer can print an average of 17.21 ppm and a standard deviation of 4 pages and its printer speed is also normally distributed. You select 10 of each printer at random. What is the probability that mean Brother print speed is at least 2 pages faster than the mean HP print speed?Suppose our random variable is the braking distance of a certain car in feet on a dry surface when going 55mph. The mean braking distance is 148 feet and the standard deviation is 2.64 feet. We randomly sample 33 braking distances from this population, what is the probability that the mean braking distance for the sample is between 147.6 feet and 150 feet?