A random sample is to be selected from a population that has a proportion of successes p = 0.64. Determine the mean and standard deviation of the sampling distribution of p for each of the following sample sizes. (Round your standard deviations to four decimal places.) (a) n = 20 mean 0.64 standard deviation 0. 1073 0.1073 (b) n = 30 mean X X standard deviation (c) n = 40 mean X X standard deviation (d) n = 60 mean X X standard deviation (e) n = 110 mean X X standard deviation (f) n = 210 mean X standard deviation XThe weights (in kg) of 452 participants are recorded. The graph and summary statistics of this data are given in the JMP Applet. JMP Applet imp ? Distributions Weight Quantiles Summary Statistics 100.0% maximum 176 Mean 68.170354 99.5% 120.29 Std Dev 16.590803 97.5% 97 Std Err Mean 0.7803657 90.0% 86 Upper 95% Mean 69.703958 75.0% quartile 79 Lower 95% Mean 66.63675 50.0% median 68 N 452 25.0% quartile 59 20 40 60 80 100 120 140 160 180 10.0% 52 2.5% 28.325 0.5% 10 0.0% minimum 6 Click here to access the JMP applet in a new window.- (a) What percentage of participants weigh less than 59 kg? 25 % How many participants (of the 452) weigh less than 59 kg? (Round your answer down to the nearest whole number.) 113 participants - (b) What percentage of participants weigh more than 79 kg? 97.5 * % How many participants (of the 452) weigh more than 79 kg? (Round your answer down to the nearest whole number.) 479.29 * participants - (c) Fill in the blanks for the following statement. Of those weights studied, the middle 99% of weights fall between a lower bound of kg and an upper bound of kg. - (d) What weight separates the smallest 50% of participants from the largest 50% of participants? kg Recall that the k" percentile is a data value that separates the lower % from the upper 100-%. Given a data value, how can the percentile be found? If there are 452 data values, how is a certainConsider selecting a household at random in the rural area of a country. Define the random variable x to be x = number of individuals living in the selected household Based on information in an article, the probability distribution of x is as given below. X 2 3 5 6 7 8 9 10 p(x) 0.140 0.177 0.220 0.260 0.153 0.026 0.014 0.005 0.004 0.001 Calculate the mean value of the random variable x. HY = Need Help? Read ItStarting at a particular time, each car entering an intersection Is observed to see whether it tums left (L) or right (R) or goes straight ahead (5). The experiment terminates as soon as a car is observed to go straight. Suppose that the random variable y denotes the number of cars observed. (a) What are possible y-values? ' all real numbers greater than 1 ' all whole numbers greater than 1 ' all Integers ' all positive whole numbers ' all positive real numbers (b) List five different outcomes and their associated y-values. Outcome Value of y RLS RRRS LRRRLS LRRLS