Q #1

Binomial probability distributions depend on the number of trials n of a binomial experiment and the probability of success p on each trial. Under what conditions is it appropriate to use a normal approximation to the binomial? (Select all that apply.) Unp>10 Ip>0.5 Up5 Inq>5 an>10 3' Need Help? Submit Answer e I II II In the following problem, check that it is appropriate to use the normal approximation to the binomial. Then use the normal distribution to estimate the requested probabilities. More than a decade ago, high levels of lead in the blood put 81% of children at risk. A concerted effort was made to remove lead from the environment. Now, suppose only 11% of children in the United States are at risk of high bloodilead levels. (a) In a random sample of 184 children taken more than a decade ago, what is the probability that 50 or more had high bloodilead levels? (Round your answer to three decimal places.) (b) In a random sample of 184 children taken now, what is the probability that 50 or more have high bloodilead levels? (Round your answer to three decimal places.) Z Need Help? In the following problem, check that it is appropriate to use the normal approximation to the binomial. Then use the normal distribution to estimate the requested probabilities. Do you try to pad an insurance claim to cover your deductible? About 35% of all U.S. adults will try to pad their insurance claims! Suppose that you are the director of an insurance adjustment office. Your ofce has just received 130 insurance claims to be processed in the next few days. Find the following probabilities. (Round your answers to four decimal places.) I2 USE SA (a) half or more of the claims have been padded 0 0002 .y (b) fewer than 45 of the claims have been padded E (c) from 40 to 64 of the claims have been padded E (d) more than 80 of the claims have not been padded Z Need Help? In the following problem, Check that it is appropriate to use the normal approximation to the binomial. Then use the normal distribution to estimate the requested probabilities. Ocean fishing for billsh is very popular in the Cozumel region of Mexico. In the Cozumel region about 41% of strikes (while trolling) resulted in a catch. Suppose that on a given day a fleet of fishing boats got a total of 27 strikes. Find the following probabilities. (Round your answers to four decimal places.) la use SA (a) 12 or fewer fish were caught S (b) 5 or more sh were caught E (c) between 5 and 12 sh were caught Z Need Help? In the following problem, check that it is appropriate to use the normal approximation to the binomial. Then use the normal distribution to estimate the requested probabilities. It is known that 76% of all new products introduced in grocery stores fail (are taken off the market) within 2 years. If a grocery store chain introduces 66 new products, find the following probabilities. (Round your answers to four decimal places.) l USE SA (a) within 2 years 47 or more fail S (b) within 2 years 58 or fewer fail E (c) within 2 years 15 or more succeed S (d) within 2 years fewer than 10 succeed Z Need Help? In the following problem, check that it is appropriate to use the normal approximation to the binomial. Then use the normal distribution to estimate the requested probabilities. What's your favorite ice cream flavor? For people who buy ice cream, the allatime favorite is still vanilla. About 22% of ice cream sales are vanilla. Chocolate accounts for only 8% of ice cream sales. Suppose that 176 customers go to a grocery store in Cheyenne, Wyoming, today to buy ice cream. (Round your answers to four decimal places.) l2 USES (a) What is the probability that 50 or more will buy vanilla? E (b) What is the probability that 12 or more will buy chocolate? S (c) A customer who buys ice cream is not limited to one container or one flavor. What is the probability that someone who is buying ice cream will buy chocolate or vanilla? Hint: Chocolate flavor and vanilla flavor are not mutually exclusive events. Assume that the choice to buy one flavor is independent of the choice to buy another avor. Then use the multiplication rule for independent events, together with the addition rule for events that are not mutually exclusive, to compute the requested probability. S (d) What is the probability that between 50 and 60 customers will buy chocolate or vanilla ice cream? Hint: Use the probability of success computed in part (c). Z Need Help? 9. [-/1 Points] DETAILS BBUNDERSTAT12 6.6.017. MY NOTES ASK YOUR TEACHER Under what minimum conditions is it appropriate to use a normal distribution to approximate the p distribution? (Select all that apply.) O nq > 5 O npq > 10 Onp > 5 O np > 30 Op > 1 On > 30 Need Help? Read ItWhat is the formula for the standard error of the normal approximation to the p' distribution? up: What is the mean of the distribution? p\": Need Help? 12. [0.45l1 Points] PREVIOUS ANSWERS BBUNDERSTAT12 6.6.020. MY NOTES ASK YOU R TEACHER PRACTICE ANOT Suppose we have a binomial experiment in which success is dened to be a particular quality or attribute that interests us. (a) Suppose n = 37 and p = 0.20. Can we approximate by a normal distribution? Why? (Use 2 decimal places.) I , 13 f be approximated by a normal random variable because both no and no exceed v I |:|. What are the values of up and 17p? (Use 3 decimal places.) if: or: (b) Suppose n : 25 and p : 0.15. Can we safely approximate p\" by a normal distribution? Why or why not? I , 13 J be approximated by a normal random variable because np does nolexceeo v ,' |:|. (c) Suppose n : 40 and p : 0.19. Can we approximate by a normal distribution? Why? (Use 2 decimal places.) rliV beappmximatedbvanomlmndomvanamebecausea |:I- What are the values of lip and Up? (Use 3 decimal places.) up : |:l Ina : Z Need Help