A box of 14 parts contains 5 that are defective. A worker picks parts one at a time and attempts to install them.

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1. Suppose x has a distribution with μ = 18 and σ = 14. (a) If a random sample of size n = 36 is drawn, find μx bar, σ x bar and P(18 ≤ x bar ≤ 20). (Round σx bar to two decimal places and the probability to four decimal places.) ux= 18 σ x= 2.33 P(18 ≤ x bar ≤ 20) = ?? (b) If a random sample of size n = 65 is drawn, find μx bar, σ x bar and P(18 ≤ x bar ≤ 20). (Round σ x bar to two decimal places and the probability to four decimal places.) μx bar = 18 σ x bar = 1.74 P(18 ≤ x bar ≤ 20) = ?? I found part of the question but can't find the last part. Please provide how you work and get the answer. 2. Coal is carried from a mine in West Virginia to a power plant in New York in hopper cars on a long train. The automatic hopper car loader is set to put 66 tons of coal into each car. The actual weights of coal loaded into each car are normally distributed, with mean μ = 66 tons and standard deviation σ = 0.5 ton. (a) What is the probability that one car chosen at random will have less than 65.5 tons of coal? (Round your answer to four decimal places.) (b) What is the probability that 20 cars chosen at random will have a mean load weight x bar of less than 65.5 tons of coal? (Round your answer to four decimal places.) 3. A random sample of 322 medical doctors showed that 162 had a solo practice. (a) Let p represent the proportion of all medical doctors who have a solo practice. Find a point estimate for p. (Use 3 decimal places.) (b) Find a 99% confidence interval for p. (Use 3 decimal places.) lower limit upper limit The method of tree ring dating gave the following years A.D. for an archaeological excavation site. Assume that the population of x values has an approximately normal distribution. 1229 1208 1285 1299 1268 1316 1275 1317 1275 (a) Use a calculator with mean and standard deviation keys to find the sample mean year x bar and sample standard deviation s. (Round your answers to the nearest whole number.) x bar = 1275 Correct: Your answer is correct. A.D. s = 37 Correct: Your answer is correct. yr (b) Find a 90% confidence interval for the mean of all tree ring dates from this archaeological site. (Round your answers to the nearest whole number.) lower limit ??? upper limit 1296