ch.86 O S.I.A. Best Songs V xO Syllabus for Statistics* Hmwk: Chapter 8 - Mat xMy Questions | bartleby x= 6.1 The Standard Norm xBookmarksA webassign.net/web/Student/Assignment-Responses/last?dep=25262768Suppose that insurance companies did a survey. They randomly surveyed 450 drivers and found that 300 claimed they always buckle up. We are interested in the populationproportion of drivers who claim they always buckle up.NOTE: If you are using a Student's t-distribution, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption,though.)O Part (a)(i) Enter an exact number as an integer, fraction, or decimal.X =(ii) Enter an exact number as an integer, fraction, or decimal.n =(iii) Round your answer to four decimal places.p'=(rounded to four decimal places)O Part (b)In words, define the random variables X and P'.O Xis the proportion of people in the sample who do not buckle up, and P'is the number of people who do not buckle up.O Xis the number of people who claim they buckle up, and P'is the proportion of people in the sample who buckle up.O Xis the number of people who do not buckle up, and P'is the proportion of people in the sample who do not buckle up.O Xis the proportion of people in the sample who claim they buckle up, and P'is the number of people who buckle up.Correct! The random variable of interest, X, is the number of people who buckle up, and P'represents the proportion of the sample who buckle up.O Part (c)Which distribution should you use for this problem? (Round your answer to four decimal places.)P'- O S.I.A. Best Songs V xO Syllabus for Statistics* Hmwk: Chapter 8 - Mat xMy Questions | bartleby x= 6.1 The Standard Norm xBookmarksA webassign.net/web/Student/Assignment-Responses/last?dep=25262768Explain your choice.O The Student's t-distribution should be used because we do not know the standard deviation.O The binomial distribution should be used because there are two outcomes, buckle up or do not buckle up.The normal distribution should be used because we are interested in proportions and the sample size is large.The Student's t-distribution should be used because V npg s 10, which implies a small sample.Correct! We use the standard normal distribution to create confidence intervals about the population proportion.O Part (d)Construct a 95% confidence interval for the population proportion who claim they always buckle up.(i) State the confidence interval. (Round your answers to four decimal places.)(ii) Sketch the graph.aC.L. =P'(iii) Calculate the error bound. (Round your answer to four decimal places.)

Part a: x = 300 n = 450 p' = 300/450 = 0.6667 Part b: X is the number of people who claim to buckle up and p' is the proportion of people in the sample who buckle up. Part c: Since the sample is large, the sampling distribution of the sample proportion is approximately normal for large samples Therefore. p' ~ N(P, PQ/n)where P is the population proportion of people who buckle up, and Q = 1 - P Part d: (i) A 95% confidence interval for the population proportion of people who buckle up is p' ± zα/2×p'q'/n= 0.6667 ± 1.96×0.6667×0.3333/450= 0.6667 ± 0.0436= 0.6231 to 0.7103 (ii) α2 = 0.52 = 0.025, C.L. = 0.95, α2 = 0.52 = 0.025 with in the limits (iii) Error bound, E is E = ± zα/2×p'q'/n = ± 1.96×0.6667×0.3333/450 = ± 0.7103