Prob & Stat Normal Curves Name_____________________________ Solve the following problems. 1. The average high school student swears an average of 32.3 times in a school day with a standard deviation of 4.8 curse words. What is the probability that a person curses less than 20 times in one school day? 2. An exclusive college desires to accept only the top 20% of all graduating seniors based on the results of a national placement test. This test has a mean of 500 and a standard deviation of 100. Find the cutoff score for the exam. 3. A car dealer finds that the average price of a previously owned car is $8276. He decides to sell cars that well appeal to the middle 60% of the market in terms of price. Find the maximum and minimum prices of the cars the dealer will sell. The standard deviation if $1200. 4. Pizzas are delivered in 19.4 minutes on average with a standard deviation of 6.2 minutes. a. What is the probability that it will take more than 22 minutes to get the pizza? b. What is the probability that it will take between 18 and 20 minutes to get a pizza? c. What is time that represents the 94th percentile of times for delivery? 5. The average American has 16 different jobs in their lifetime with a standard deviation of 4.3 jobs. The middle 55% of Americans will have somewhere between how many jobs? 6. MTV just piloted a new show called Extreme Polka Dancing. In order for the show to be picked up by the network, the pilot has to score in the top 33% of MTV’s new show viewer ratings. On average, MTV’s new shows score a 720 in the ratings with a standard deviation of 32. What rating does the pilot episode of Extreme Polka Dancing have to get in order to be picked up for circulation? 7. The mean salary of high school teachers in the United States is $38,867 with a standard deviation of $3000. What is the probability that a randomly selected teacher makes more than $42,000 if the distribution of salaries is approximately normal? 8. The average hourly wage of production workers in manufacturing is $13.76 with a standard deviation of $2.72. If the distribution of wages is approximately normal, what is the probability of randomly selecting a manufacturer worker who makes at most $12.89 per hour? 9. A brisk walk at 4 mph burns an average of 300 calories per hour. If the standard deviation of the distribution is 8 calories, find the probability that a person who walks one hour at the rate of 4 mph will burn between 285 and 320 calories. Assume the distribution is approximately normal. 10. In order to qualify for police academy training, recruits are tested for stress tolerance. The scores are normally distributed, with a mean of 60 and a standard deviation of 10. If only the top 20% of recruits are selected, find the cutoff score. 11. A pet shop owner decides to sell tropical fish that will appeal to the middle 60% of customers. The owner reads in a study that the mean price of tropical fish sold is $9.52 with a standard deviation of $1.02. Find the maximum and minimum prices of tropical fish the owner should sell. Assume the variable is normally distributed.