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- The Food Marketing Institute shows that 16% of households spend more than $100 per week on groceries. Assume the population proportion is p = 0.16 and a sample of 800 households will be selected from he population. Use z-table. a. Calculate o (P), the standard error of the proportion of households spending more than $100 per week on groceries (to 4 decimals). . What is the probability that the sample proportion will be within +/- 0.02 of the population proportion (to 4 decimals)? . What is the probability that the sample proportion will be within +/- 0.02 of the population proportion for a sample of 1,500 households (to 4 decimals)?3. Find a z value such that the probability of obtaining a larger z value is only 0.15.Sean thinks that he has a special relationship with the number 6. In particular, Sean thinks that he would roll a 6 with a fair 6-sided die more often than you'd expect by chance alone. Suppose pis the true proportion of the time Sean will roll a 6. (a) State the null and alternative hypotheses for testing Sean's claim. (Type the symbol "p" for the population proportion, whichever symbols you need of "", "-", "not =" and express any values as a fraction e.g. p = 1/3) Ho= Ha (b) Now suppose Sean makes n = 30 rolls, and a 6 comes up 6 times out of the 30 rolls. Determine the P-value of the test, giving your answer to 4 decimal places. Please use 3 decimal places in your test statistic when finding the P-value. P-value = ⠀⠀ (c) Answer the question: Does this sample provide evidence at the 5 percent level that Sean rolls a 6 more often than you'd expect? (Type: Yes or No) 4
- H.W :A study determined that the difference between the quoted to women and men for used cars is normally distributed with mean $ 400 and standard price f(x) deviation $50. let X be the amount quoted to a woman minus the amount quoted to a man for a given used car, find The probability P(275 < X < 500) that is shown as the shaded area in Fig. 6-20. 275 400 500Match the following questions with the correct answers. A. 24 B. 0.0929 C. 2 D. 154 E. 3/4 F. 120 select select select select select select 1. If X220, the probability that a man aged x marries at time t from the present is 15dt/(t+x)2. Find the probability that a person aged 20 eventually marries. 2. If X is the number of 6's which appear when 72 dice are thrown, what is the expected value of X²? 3. Suppose only 12% of men in ancient Greece were honest. What is the probability that the first honest man Diogenes Jencounters will be the third man he meets? 4. Find the expected value of the number of times one must throw a die until the outcome 1 has occurred 4 times? 5. Find the variance value of the number of times one must throw a die until the outcome 1 has occurred 4 times? 6. If for a Poisson distribution 2f(0)+f(2)=2f(1), what is the variance of the distribution?Matt thinks that he has a special relationship with the number 2. In particular, Matt thinks that he would roll a 2 with a fair 6-sided die more often than you'd expect by chance alone. Suppose p is the true proportion of the time Matt will roll a 2. (a) State the null and alternative hypotheses for testing Matt's claim. (Type the symbol "p" for the population proportion, whichever symbols you need of "", "=", "not =" and express any values as a fraction e.g. p = 1/3) Ho p= 1/6 = Ha= p > 1/6 (b) Now suppose Matt makes n = 34 rolls, and a 2 comes up 7 times out of the 34 rolls. Determine the P-value of the test: P-value = | (c) Answer the question: Does this sample provide evidence at the 5 percent level that Matt rolls a 2 more often than you'd expect? (Type: Yes or No) no
- Use the following information to answer A-C. The table below shows the probablity of a certain number of students having fatigue. (Out of 4 randomly selected students)/ x P(x) 0 0.10 1 0.20 2 0.35 3 0.30 4 0.05 A) What is the probability that more than 2 of 4 randomly selected students have fatigue? B) What is the mean (to the nearest 0.1) number of students with fatigue out of 4 randomly selected students? C) What is the standard deviation (to the nearest 0.1) of the number of students with fatigue out of 4 randomly selected students? [Show all work with a table or formula]2. The number of meteors found by a radar system in any 30-second interval under specified a. What is the probability that at least one meteor is found in a one-minute interval? ne meteors appear randomly b. Determine x such that the probability no meteor is found in x-minute interval is 0.02. UTM M UTM UTM c. If there is no meteor appear after two-minute interval, what is the probability that it UTM will appear in the next one and a half-minute interval? m UTM3. Determine each of the following areas and show these graphically. Use probability notation in you final answer. a. above z = 1.46 b. between z = 2.20 and z =1.00 4. The IQ scores of children in a special education class are normally distributed with = 95 and = 10. a. What is the probability that one of the children has an IQ score below 100? b. What is the chances that a child has an IQ score of 90? 5. A electrical company claims that the average life of the bulbs it manufactures is 1,200 hours with a standard deviation of 250 hours. If random sample of 100 bulbs is chosen, what is the probability that the sample mean will be: a. greater than 1,150 hours? b. less than 1,250 hours?
- The 2010 U.S. Census found the chance of a household being a certain size. The data is in the pmf below ("Households by age," 2013). Let X be the number (size) in a household. E(X) = k·P(X = k) 7 (or more) P(X=k) 0.267 0.336 0.158 0.137 0.063 0.024 0.015 k 1 2 3 5 6 a) The probability of a household size being more than 5, P(X > 5) = % b) In the long run, we are expected to see a household size of, E(X)= on average. Round answer to three decimal places. c) The probability that the size of a household is equal to two is %. d) The probability of a household size being three OR six is %.E is an event and P(not E) = 0.4. Find P(E).23. Flip six unfair coins where, for each coin, P(H) = 0.20 and P(T)= 0.80. Let X be the total number of heads. Find P(X = 4), the probability of getting 4 heads. A. 0.04536 %3D B. 0.03536 C. 0.02536 D. 0.01536