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2. Consider the following probability distribution function of the random variable X which represents x the number of people in a group (party) at a restaurant: P(X) 1 0.10 2 0.25 3 0.20 4 0.20 5 0.10 6 7 0.05 8 0.05 with 3. 10% of disabilities. all children 10 at children large urban are randomly elementary and school independently district have selected been diagnosed from this school learning district. 4. A general the truthfulness of this figure for a particular retail store, say store A. also statement is made that an error occurs in 10% of all retail transactions. Twenty We wish to transactions evaluate of this store are randomly obtained. Assuming that the the 10% sample figure applies to store A and let x be the number of retail transactions with errors in 5. A newspaper finds a mean of 4 typographical errors per page. Assume the errors follow a Poisson distribution. 5. A deviation normally of distributed 12.2 g. population of package weights has a mean of 63.5 g and a standard 6. earthquake Assume the expected waiting time until the next RM (Richter somewhere in California follows an exponential distribution Magnitude) with 7.0 u or = greater 10 years. 7. High Fructose Corn Syrup (HFCS) is a sweetener in food products that is linked to obesity and type II diabetes. The mean annual consumption in the United States in 2008 of HFCS was 60 lbs with a standard deviation of 20 lbs. Assume the population follows a Normal Distribution. accidents Major accidents at a regional refinery occur on the average once every five years. Assume 6. follow a Poisson distribution. the 7. 20% of the people in a California town consider themselves vegetarians. If 20 people are randomly sampled, find the probability that: 8. State in your own words the 3 important parts of the Central Limit Theorem. 9. For women aged 18-24, systolic blood pressures (in mmHg) are normally distributed with H= -114.8 and o=13.1. handling 8. Cargo ships 3 arrivals arrive at a loading dock at a rate of 2 per day. The dock has the capability of more than to handle all arriving ships? (Hint: first find the probability that expect the dock being per unable day. How many days per month (assume 30 days in a month) would you month too many ships arrive.) 3 ships arrive and then use that probability to find the expected number of days in a CONTINOUS DISTRIBUTION 2. A ferry boat leaves the dock once per hour. Your waiting time for the next ferryboat will follow a uniform distribution from 0 to 60 minutes. 3. The cycle times for a truck hauling concrete to a highway construction site are uniformly distributed over the interval 50 to 70 minutes. 10. The following data represents 20 random samples from a discrete uniform distribution S={1,2,3,4,5,6,7,8,9). The sample mean (x) was calculated for each group: Math 10 - Homework 2 Illowsky's problems in Use knowing the following what information to answer the next seven exercises: A ballet instructor is interested classes to offer. percent each year's class will continue on to the next, so that she can plan what Over the years, she has established the following probability distribution. 72. You four available $25 to be buy sold a lottery in this ticket lottery. to a In lottery this that costs $10 per ticket. There are only 100 tickets prizes. Find your expected gain or lottery loss. there Do you are still one want $500 to prize, play two raffle? $100 prizes, and DISCRETE DISTRIBUTION 1. Explain the difference between population parameters and sample statistics. What symbols do we use for the mean and standard deviation for each of these?

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