Here is the setup for a non-traditional dice game: You roll a die and if the die is a 6 you win $100. The game costs $5 to play and you decide to play the game until you win the 5100. Each time you roll a die you pay $5, and if it is not a 6, you lose your $5. How much money should you expect to spend on this game? The number of chocolate chips in a cholate chip cookie has a bell-shaped distribution. This distribution has a mean of 12 and a standard deviation of 4. Using the empirical rule (as presented in the book), what is the approximate percentage cookies numbering between 4 and 24? (Round percent number to 2 decimal places.) ans = 96 The heights of adult men in America are normally distributed, with a mean of 69.9 inches and a standard deviation of 2.71 inches. The heights of adult women in America are also normally distributed, but with a mean of 64.9 inches and a standard deviation of 2.61 inches. a) If a man is 6 feet 2 inches tall, what is his z-score (to two decimal places)? b) If a woman is 5 feet 6 inches tall, what is her z-score (to two decimal places)? c) Who is relatively taller? O The 6 foot 2 inch American man O The 5 foot 6 inch American woman A large company knows that replacement times for the calculators it produces are normally distributed with a mean of 2.6 years and a standard deviation of 0.4 years. Find the probability that a randomly selected calculators will have a replacement time less than 1.3 years? Write your answer accurate to 4 decimal places. A large company knows that replacement times for the calculators it produces are normally distributed with a mean of 10 years and a standard deviation of 1.3 years. If the company wants to provide a warranty so that only 2.5% of the calculators will be replaced before the warranty expires, what is the time length of the warranty? (Write your answer as a number accurate to 1 decimal place.) When taking a 9 question multiple choice test, where each question has 4 possible answers, it would be unusual to get or more questions correct by guessing alone. Give your answer as a whole number. (Assume that the threshold for an "unusual" event is considered to be one that has a likelihood of 5% or less. Hint: Try starting around x=6.) A survey is conducted and the data is summarized in the following table: Has Children Based on this data: (give your answers to as fractions, or decimals to at least 3 decimal places.) a) The proportion of people surveyed that own a house is: b) Assume that this proportion is true for ALL people (e.g. that this proportion applies to any group of people). If 7 people are chosen, the probability that exactly 3 would own a house: Grades on a test have a mean of 72.0 and a standard deviation of 6.2. Find the test score of a student with a z-score of 0.9 (to 2 decimal places) The time it takes me to go grocery shopping is uniformly distributed between 96 minutes and 204 minutes. What is the probability that grocery shopping tonight will take me between 181 and 203 minutes? Give your answer accurate to two decimal places. The probability density of a random variable X is given in the figure below. 012345678910 From this density, the probability that X > 5.3 or X 0.05) Express the probability as a decimal rounded to 4 decimal places. A particular fruit's weights are normally distributed, with a mean of 478 grams and a standard deviation of 9 grams. If you pick one fruit at random, what is the probability that it will weigh between 447 grams and 457 grams? The heaviest 15% of fruits weigh more than how many grams? The average price of a college math textbook is $158 and the standard deviation is $29. Suppose that 15 textbooks are randomly chosen. Round all answers to 4 decimal places where possible. a. What is the distribution of (E? .17: ~ N( , ) b. For the group of 15, find the probability that the average price is between $164 and $173. c. Find the first quartile for the average textbook price for this sample size. 5 (round to the nearest cent) d. For part b), is the assumption that the distribution is normal necessary? O NoO Yes A population of proportions has a distribution with p = 0.3 and 0' = 0.458. You intend to draw a random sample of size n = 11. According to the Central Limit Theorem: What is the mean of the distribution of sample means? A p: What is the standard deviation of the distribution of sample means? (Report answer accurate to 3 decimal places.) 0'15: Approximately 10% of all people are left-handed ("11 little-known facts," 2013). Consider 16 randomly selected people. a.) Explain why this is a binomial experiment. Check all that apply. [3 Whether or not one randomly selected person is left-handed will not affect whether or not another randomly selected person is left-handed [:1 p = 10% remains constant from one randomly selected person to another [3 There is not a fixed number of person(s) [:1 Whether or not one randomly selected person is left-handed will affect whether or not another randomly selected person is left-handed [3 There are only two outcomes for each person(s) Q There are more than two outcomes for each person(s) Q There are a fixed number of person(s) Find the probability, to 4 decimal places: b.) exactly none are left-handed. c.) exactly 8 are left-handed. d.) at least 5 are left-handed. e.) at most 7 are left-handed. f.) at least 6 are left-handed. i g.) Is 6 an unusually high number of left-handed people in a group of 16? 0 Yes because P(X>=6)>0.05 0 Yes because P(X0.05 O No because P(X>=6)0.05 0 Yes because P(X=6) >0.05 0 Yes because P(X>=6)=6)>0.05 O No because P(X=6) >0.05 0 Yes because P(X=6)