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Instruction: 1. Identify distributions as symmetric or skewed. 2. Identify the properties of a normal distribution. 3.Find the area under the standard normal distribution, given various z values. 4.Find probabilities for a normally distributed variable by transforming it into a standard normal variable. 5.Find specific data values for given percentages, using the standard normal ditribution. 6.Use the central limit theorem to solve problems involving sample means for large samples. Use the normal approximation to compute probabilities for a binomial variable. DOWN BELOW ARE THE QUESTIONS 1. Admission Charge for Movies The average early-bird special admission price for a movie is $5.81. If the distribution of movie admission charges is approximately normal with a standard deviation of $0.81, what is the probability that a randomly selected admission charge is less than $3.50? 0.0022 2. Teachers' Salaries The average annual salary for all U.S. teachers is $47,750. Assume that the distribution is normal and the standard deviation is $5680. Find the probability that a randomly selected teacher earns a. Between $35,000 and $45,000 a year 0.3031 b. More than $40,000 a year 0.9131 c. If you were applying for a teaching position and were offered $31,000 a year, how would you feel (based on this information)? Not too happy?it's really at the bottom of the heap! (prob. 0.0016) Source: New York Times Almanac. 3. Population in U.S. Jails The average daily jail population in the United States is 706,242. If the distribution is normal and the standard deviation is 52,145, find the probability that on a randomly selected day, the jail population is a. Greater than 750,000 0.2005 (TI: 0.2007) b. Between 600,000 and 700,000 0.4315 (TI: 0.4316) Source: New York Times Almanac. 4. SAT Scores The national average SAT score (for Verbal and Math) is 1028. If we assume a normal distribution with s 92, what is the 90th percentile score? What is the probability that a randomly selected score exceeds 1200? 1146; 0.0307 Source: New York Times Almanac. 5. Chocolate Bar Calories The average number of calories in a 1.5-ounce chocolate bar is 225. Suppose that the distribution of calories is approximately normal with s 10. Find the probability that a randomly selected chocolate bar will have a. Between 200 and 220 calories 0.3023 b. Less than 200 calories 0.0062 Source: The Doctor's Pocket Calorie, Fat, and Carbohydrate Counte

Which of the following is TRUE about a population that is NOT normally distributed? l{Eluestion 8 options: Central limit theorem can be used if the sample size is large enough. Central limit theorem says that sample standard deviation will be equal to population standard deviation for large enough samples. Central limit theorem guarantees normal distribution of sample means for any sample size. Central limit theorem cannot be used ariate Normal Distribution: Correlation Correlation of Bivariate Normal Random Variables If X and Y have a bivariate normal distribution with joint probability density function fxr(x, y, Gx, Gy, Hx, Hy, P), the correlation between X and Y is p. (5.23) For Bivariate Normal Random Variables Zero Correlation Implies Independence If X and Y have a bivariate normal distribution with p = 0, then X and Y are independent. (5.24)Question 21 4 If you don't know whether the frequency distribution is normally distributed. O You can use both the Empirical Rule and the Central Limit Theorem O You can't use the Empirical Rule, but you can use the Central Limit Theorem O You can't use the Central Limit Theorem, but you can use the Empirical Rule You can't use either the Empirical Rule or the Central Limit Theorem