Please solve
7. [0.2!0.42 Points] BBUNDERSTAT126.6.011. 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 85% of all new products introduced in grocery stores fail (are taken off the market) within 2 years. If a grocery store chain introduces 60 new products, nd the following probabilities. (Round your answers to four decimal places.) (a) within 2 years 47 or more fail |o.9434 | I (b) within 2 years 58 or fewer fail |0.9966 | v (0) within 2 years 15 or more succeed |o.0291 | x (d) within 2 years fewer than 10 succeed |o.5a77 | x \\ 5. [0.271053 Points] BBUNDERSTAT12 6.6.009.Ml. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER 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 estimated that 3.5% of the general population will live past their 90th birthday. In a graduating class of 763 high school seniors, nd the following probabilities. (Round your answers to four decimal places.) (a) 15 or more will live beyond their 90th birthday 0.9910 J (b) 30 or more will live beyond their 90th birthday 0.2912 v (c) between 25 and 35 will live beyond their 90th birthday 0.6248 I (d) more than 40 will live beyond their 90th birthday 0.0052 X 4. [0.181038 Points] BBUNDERSTAT126.6.00B. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER 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 45% of all US. adults will try to pad their insurance claims! Suppose that you are the director of an insurance adjustment ofce. Your office has just received 120 insurance claims to be processed in the next few days. Find the following probabilities. (Round your answers to four decimal places.) (a) half or more of the claims have been padded l0.1562 | I X (lbi fewer than 45 of the claims have been padded (c) from 40 to 64 of the claims have been padded l0.9691 | v (d) more than 80 of the claims have not been padded |o.oooo | x l=ll=l Step 1 (a) If specifications for a research project require the standard error of the corresponding x distribution to be 7, how large does the sample size need to be? Recall that the standard deviation (also known as the standard error) of the x distribution iS of= - where O is the standard deviation of the x distribution. Find the sample size n for the research project given that - = 7 and o = 70. OF = Vn 70 7 n Vn = 100 X n = 4900 X3. [0.111022 Points] BBUNDERSTAT12 6.5.007. MY NOTES ASK YOUR TEACHER (a) If we have a distribution ofx values that is more or less mound-shaped and somewhat symmetric, what is the sample size n needed to claim that the distribution of sample means x from random samples of that size is approximately normal? n21 |x (b) If the original distribution ofx values is known to be normal, do we need to make any restriction about sample size in order to claim that the distribution of sample means )7 taken from random samples of a given size is normal? Yes 12. [0.130.16 Points] BBUNDERSTAT126.3.026. Porphyrin is a pigment in blood protoplasm and other body \" uids that is signicant in body energy and storage. Let X be a random variable that represents the number of milligrams of porphyrin per deciliter of blood. In healthy circles, X is approximately normally distributed with mean it = 39 and standard deviation 0 = 9. Find the following probabilities. (Round your answers to four decimal places.) (a) X is less than 60 0.9902 J (b) X is greater than 16 0.9946 I (c) X is between 16 and 60 0.93m x (d) X is more than 60 (This may indicate an infection, anemia, or another type of illness.) 0.0099 V Look at the normal curve below, and find u, u + o, and o. 66 69 72 75 Step 1 First find M. Recall that a normal curve is bell-shaped with the highest point over the mean, M. 66 69 72 75 Observing the given normal curve we see that the highest point is located when x = 75 X . Therefore, U = 66Step 2 Since 29 is two standard deviations to the left of u and 33 is two standard deviations to the right of u, we need to find the area under the normal curve from u- " to u + 20. Area Under a Normal Curve 2.35% 13.5% 34% 34% 13.5% 2.35% H - 30 1 - 20 4-0 LL uto u+ 20 u+ 30 68% 95% 99.7% Referring to the figure above, we see that % of the area under the curve falls between these values. Therefore, % of the 10,000 chicks can be expected to hatch in 29 to 33 days. In other words, we expect eggs to hatch during this time period
