6.1 Continuous vs. Discrete

6.2 The Frequency Polygon

6.3 The Normal Curve

6.4 Z-scores, Percentiles and Probabilities

Continuous Probability Dlstrlhutlon: Tho Normal Distribution Show all processes. 1. Mikasa is a branch manager and decided to work on the time that any customer wait to get their work done at banks. Mikasa collected the following results: 9, 11, 3, 6, 8, 20, 12, 25, 4, 6, 7, 4, 10, 12, 14, 16, 21, 21, 25, 30, 22, 10, 7, 8, 5. a) Construct a frequency table (include cumulative frequency) for Mikasa's data. b) Construct a histogram graph, frequency polygon graph, and cumulative-frequency diagram (plot on the same grid). 2. The heights of two types of creatures, Digimon and Pokemon, are normally distributed. Pokemon have an average height of 68.5 inches with a standard deviation of 2.7 inches. Digimon have an average height of 65.6 inches and a standard deviation of 2.5 inches. a. Agumon is a Digimon and is 3 standard deviations above the average height. How tall is it? b. Arcanine is a Pokemon and is 74 inches tall. How many standard deviations above the average height is it? c. Gatomon (Digimon) is 68 inches tall. Dratini (Pokemon) is 71 inches tall. i. Calculate their z-scores ii. Who is relatively taller for their creature type? Explain your reasoning.4. The length of time a full-length movie runs from opening to credits is normally distributed with a mean of 1.9 hours and standard deviation of 0.3 hours. Calculate the following: a. A movie is longer than 2.3 hours. b. The length of a movie that is shorter than 94% of the movies. 5. The Weights of 100 remote control cars at a competition are approximately normally distributed. The average weight is 3.2 kg, with a standard deviation of 0.4 kg. a. How many remote-control cars would be disqualied if it were against the rules to have a car with a weight of more than 4 kg or less than 2.4 kg? b. A car is said to be in the 90th percentile. How much does it weigh? 3. Answer the following questions using the zscore chart. a. For a mean of 20 and standard deviation of 5, nd P(X S 17). b. For a mean of 75 and a standard deviation of 3, nd P(X 2 77). c. For a mean of 153 and standard deviation of 25, find P(130 <_: x s sketch a rough normal distribution curve we did in to illustrate yourstyle="">