1. The height of a randomly selected five-year-old child is a normal distribution with a mean of 100 cm and a standard deviation of 6 cm. a. What percent of the heights is below 87 cm? b. What percent of the heights is taller than 110 cm? c. What percent of the heights is between 94 and 112 cm?
2. IQ scores are normally distributed with a mean of 100 and a standard deviation of 15. a. What percent of people have an IQ greater than 130? b. What percent of people have an IQ less than 80? c. What percent of people have an IQ between 75 and 125?
3. Babies' birth weights in the United States are normally distributed with mean 3432 g and standard deviation 482 g. a. What is the probability that the birth weight of a randomly selected baby exceeds 4000 g? b. What is the probability that the birth weight of a randomly selected baby is between 3000 and 4000 g? c. What is the probability that the weight is less than 2000 g?
4. Bottles of eye drops are normally distributed with a mean volume of 5 ml and a standard deviation of 0.2 ml. Stores receive the eye drops in boxes containing 500 bottles. a. How many bottles in one box are predicted to be greater than 4.5 ml? b. How many bottles in one box are predicted to be less than 5.1 ml? c. How many bottles in one box are predicted to be between 4.8 and 5.3 ml?
5. Corks for wine bottles are cut by a machine that makes the diameters of each cork normally distributed with a mean of 3 cm and standard deviation of 0.1 cm. a. About what percent of the corks have a diameter less than 2.85 cm? b. In a group of 75 corks, how many would you expect to have a diameter greater than 3.25? c. In a group of 325 corks, how many would you expect to between 2.92 and 3.15 cm?
6. The average gas tank volume in the United States is normally distributed with a mean of 15 gallons and a standard deviation of 1 gallon. a. What is the probability that a tank will hold at most 14.4 b. gallons? What is the probability that the tank will hold between 13.7 and 17.1 gallons? c. Suppose you have a group of 600 tanks, how many should hold at least 16.5 gallons?
7. The time it takes a randomly selected job applicant at Collector's Edition Entertainment to load the equipment van is normally distributed with a mean of 45 minutes and a standard deviation of 5 minutes. Suppose 18 people apply for the job. a. How many job applicants will take more than 53 minutes to load the van? b. How many job applicants will be quicker than 38 minutes? c. How many will take between 39 and 58 minutes?
8. Suppose that the distribution of net typing rate in words per minute (wpm) for experienced typists can be approximated by a normal curve with mean 60 wpm and standard deviation 15 wpm. a. What is the probability that a randomly selected typist's rate is at most 70 wpm? b. What is the probability that a typist's rate is at least 50 wpm? c. What is the probability that it is between 40 and 80 wpm?
9. A pizza company advertises that it puts 0.5 lb of real mozzarella cheese on its large pizzas. The amount of cheese on a randomly selected large pizza is normally distributed with a mean of 0.5 lb and a standard deviation of 0.025 lb. Suppose Mrs. Williams orders 20 pizzas for a class party. a. How many will have less than 0.404 lb of mozzarella? b. How many will have between 0.45 and 0.53 lb of mozzarella? c. How many will have more than 0.503 lb of mozzarella?
10. Honda Civics have an average fuel efficiency of 30 mpg and a standard deviation of 1.2 mpg a. What percent of these cars have fuel efficiencies between 29 and 31 mpg? b. What percent have fuel efficiencies less than 25 mpg? c. What percent have fuel efficiencies that exceed 32 mpg?