The Normal Distributions BPS 7e Chapter 3 © 2014 W. H. Freeman and Company

Density Curves Which one of the following is a FALSE statement about density curves? Always on or above the x-axis. Area under the curve within an interval is the proportion of values expected in that interval. Total area under the curve depends on the shape of the curve. The curve is an idealized depiction of the distribution of a variable.

Density Curves (answer) Which one of the following is a FALSE statement about density curves? Always on or above the x-axis. Area under the curve within an interval is the proportion of values expected in that interval. Total area under the curve depends on the shape of the curve. The curve is an idealized depiction of the distribution of a variable.

Density Curves Which one of the following is a FALSE statement about density curves? The median divides the area under the curve in half. The mean is the balancing point of the density curve. The mean and the median are always the same number.

Density Curves (answer) Which one of the following is a FALSE statement about density curves? The median divides the area under the curve in half. The mean is the balancing point of the density curve. The mean and the median are always the same number.

Density Curves If you knew that  = 0 and  = 3, which density curve applies? Curve 1 Curve 2

Density Curves (answer) If you knew that  = 0 and  = 3, which density curve applies? Curve 1 Curve 2

Density Curves Here is a density curve as a model for the distribution of spoilage times of a packaged product. Is the mean spoilage time smaller than the median spoilage time? yes no

Describing Density Curves (answer) Here is a density curve as a model for the distribution of spoilage times of a packaged product. Is the mean spoilage time smaller than the median spoilage time? yes no

Normal Distributions Here is a normal density curve as a model for the distribution of birth weights of full-term babies in the United States. True or False: Baby Emma, who weighed 4350 g at birth, was larger than half of newborn babies. True False

Normal Distributions (answer) Here is a normal density curve as a model for the distribution of birth weights of full-term babies in the United States. True or False: Baby Emma, who weighed 4350 g at birth, was larger than half of newborn babies. True False

Normal Distributions Here is a normal density curve as a model for the distribution of birth weights of full-term babies in the United States. The median full-term birth weight is 3485 g. What is mean full-term birth weight? less than 3485 equal to 3485 greater than 3485

Normal Distributions (answer) Here is a normal density curve as a model for the distribution of birth weights of full-term babies in the United States. The median full-term birth weight is 3485 g. What is mean full-term birth weight? less than 3485 equal to 3485 greater than 3485

68-95-99.7 Rule Attendance at a university’s basketball games follows a normal distribution with mean  = 8,000 and standard deviation  = 1,000. Estimate the percentage of games that have between 7,000 and 9,000 people in attendance. 68% 95% 99.7%

68-95-99.7 Rule (answer) Attendance at a university’s basketball games follows a normal distribution with mean  = 8,000 and standard deviation  = 1,000. Estimate the percentage of games that have between 7,000 and 9,000 people in attendance. 68% 95% 99.7%

68-95-99.7 Rule SAT scores follow a normal distribution with mean  = 500 and standard deviation  = 100. Estimate the percentage of SAT scores that have between 300 and 700 points. 68% 95% 99.7%

68-95-99.7 Rule (answer) SAT scores follow a normal distribution with mean  = 500 and standard deviation  = 100. Estimate the percentage of SAT scores that have between 300 and 700 points. 68% 95% 99.7%

68-95-99.7 Rule Birth weights of full-term babies in the United States approximately follow the normal distribution with m = 3485 and s = 425. What percent of full-term babies have weights greater than 2635 g? 97.5% 84% 68% 50%

68-95-99.7 Rule (answer) Birth weights of full-term babies in the United States approximately follow the normal distribution with m = 3485 and s = 425. What percent of full-term babies have weights greater than 2635 g? 97.5% 84% 68% 50%

Standard Normal Distribution Which one of the following is a FALSE statement about the normal distribution? The mean is greater than the median. It is symmetric. It is bell-shaped. It has one peak.

Standard Normal Distribution (answer) Which one of the following is a FALSE statement about the normal distribution? The mean is greater than the median. It is symmetric. It is bell-shaped. It has one peak.

Standard Normal Distribution All Normal distributions satisfy the 68 - 95 - 99.7 rule, which describes what percent of observations lie within one, two, and five standard deviations of the mean, respectively. True False

Standard Normal Distribution (answer) All Normal distributions satisfy the 68 - 95 - 99.7 rule, which describes what percent of observations lie within one, two, and five standard deviations of the mean, respectively. True False

Standard Normal Distribution Which one of the following is a TRUE statement about the standard Normal distribution? The standard Normal distribution is the Normal distribution N(0; 1) with mean 0 and standard deviation 1. The mean and the median are not always the same in standard Normal distributions. While it mostly has one peak, it can have up to three peaks. Its mean  is constant at 1.

Standard Normal Distribution (answer) Which one of the following is a TRUE statement about the standard Normal distribution? The standard Normal distribution is the Normal distribution N(0; 1) with mean 0 and standard deviation 1. The mean and the median are not always the same in standard Normal distributions. While it mostly has one peak, it can have up to three peaks. Its mean  is constant at 1.

Standard Normal Distribution Suppose the lengths of sport-utility vehicles (SUV) are normally distributed with mean  = 190 inches and standard deviation  = 5 inches. Marshall just bought a brand new SUV that is 194.5 inches long, and he is interested in knowing what percentage of SUVs is longer than his. Using his statistical knowledge, he drew a normal curve and labeled the appropriate area of interest. Which picture best represents what Marshall drew? Plot A Plot B

Standard Normal Distribution (answer) Suppose the lengths of sport-utility vehicles (SUV) are normally distributed with mean  = 190 inches and standard deviation  = 5 inches. Marshall just bought a brand new SUV that is 194.5 inches long, and he is interested in knowing what percentage of SUVs is longer than his. Using his statistical knowledge, he drew a normal curve and labeled the appropriate area of interest. Which picture best represents what Marshall drew? Plot A Plot B

Standard Normal Distribution Which one of the following is a FALSE statement about a standardized value (z-score)? It represents how many standard deviations an observation lies from the mean. It represents in which direction an observation lies from the mean. It is measured in the same units as the variable.

Standard Normal Distribution (answer) Which one of the following is a FALSE statement about a standardized value (z-score)? It represents how many standard deviations an observation lies from the mean. It represents in which direction an observation lies from the mean. It is measured in the same units as the variable.

Finding Proportions What percentage of values of a variable following the standard normal distribution is between z-scores of 0 and 3? ~33.2% ~49.5% ~90.7% ~94.5%

Finding Proportions (answer) What percentage of values of a variable following the standard normal distribution is between z-scores of 0 and 3? ~33.2% ~49.5% ~90.7% ~94.5%

Finding Values Consider a Normal model that describes student scores in a chemistry class. Feyza has a standardized score (z-score) of +2.5. This means that Feyza is 2.5 points above average for the class. is 2.5 standard deviations above average for the class. has a standard deviation of 2.5. has a score that is 2.5 times the average for the class. None of the above.

Finding Values (answer) Consider a Normal model that describes student scores in a chemistry class. Feyza has a standardized score (z-score) of +2.5. This means that Feyza is 2.5 points above average for the class. is 2.5 standard deviations above average for the class. has a standard deviation of 2.5. has a score that is 2.5 times the average for the class. None of the above.