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A data set lists weights (Ib) of plastic discarded by households. The highest weight is 5.12 lb, the mean of all of the weights is x = 2.032 lb, and the standard deviation of the weights is s = 1.807 lb. a. What is the difference between the weight of 5.12 lb and the mean of the weights? b. How many standard deviations is that [the difference found in part (a)]? c. Convert the weight of 5.12 lb to a z score. d. If we consider weights that convert to z scores between - 2 and 2 to be neither significantly low nor significantly high, is the weight of 5.12 lb significant? a. The difference is |Ib. (Type an integer or a decimal. Do not round.) b. The difference is standard deviations. (Round to two decimal places as needed.) c. The z score is z = (Round to two decimal places as needed.) d. The highest weight isHouseholds are randomly selected and partitioned into groups of four. For those groups, the random variable x is the number of households with a printer. Determine whether a probability X P(x) distribution is given. If a probability distribution is given, find its mean and standard deviation. If a probability distribution is not given, identify the requirements that are not satisfied. 0 0.027 1 0.147 2 0.336 3 0.354 4 0. 136 Does the table show a probability distribution? Select all that apply. A. Yes, the table shows a probability distribution. B. No, not every probability is between 0 and 1 inclusive. C. No, the random variable x is categorical instead of numerical. D. No, the numerical values of the random variable x are not associated with probabilities. OE. No, the sum of all the probabilities is not equal to 1. Find the mean of the random variable x. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. H= household(s) (Round to one decimal place as needed.) O B. The table does not show a probability distribution. Find the standard deviation of the random variable x. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. 6= household(s) (Round to one decimal place as needed.) O B. The table does not show a probability distribution.Heights (cm) and weights (kg) are measured for 100 randomly selected adult males. and range from heights of 135 to 192 cm and weights of 33 to 150 kg. Let the predictor variable x be the first variable given. The 100 paired measurements yield 32:16730 cm, =81.42 kg, r: 0.299, Pvalue = 0 003, and = 101 +1.02x Find the best predicted value of; (weight) given an adult male who is 190 cm tall. Use a 0.10 signicance level. The best predicted value of; for an adult male who is 190 cm tall is kg. (Round to two deCimal places as needed.) Construct the cumulative frequency distribution for the given data. Age (years) of Best Actress when award was won Cumulative Frequency Age (years) of Best Actress when award was won Frequency Less than 30 20-29 26 30-39 37 Less than 40 40-49 12 Less than 50 50-59 Less than 60 60-69 70-79 Less than 70 80-89 Less than 80 Less than 90The body temperatures of a group of healthy adults have a bell-shaped distribution with a mean of 98.05 F and a standard deviation of 0.67 F. Using the empirical rule, find each approximate percentage below. a. What is the approximate percentage of healthy adults with body temperatures within 3 standard deviations of the mean, or between 96.04 F and 100.06 F? b. What is the approximate percentage of healthy adults with body temperatures between 96.71 F and 99.39 F? a. Approximately |% of healthy adults in this group have body temperatures within 3 standard deviations of the mean, or between 96.04 F and 100.06 F. (Type an integer or a decimal. Do not round.) b. Approximately |% of healthy adults in this group have body temperatures between 96.71 F and 99.39 F. (Type an integer or a decimal. Do not round.)The sample space listing the eight simple events that are p055ible when a couple has three Children is {[1be bbg' bgb, bgg, glib, ghg, ggb, ggg}, Alter Identifying the sample space for a couple having four children, nd the probability of getting one girl and three boys (in any order), Identify the sample space fora couple having four children, { l (Use a comma to separate answers as needed) Find the probability of getting one girl and three boys (in any order). (Type an integer or a decimal, Do not round} Listed below are the numbers of words spoken in a day by each member of eight different randomly selected couples. Complete parts (a) and (b) below. Male 16,046 27,327 1421 7617 18,446 14,904 13,778 26,466 Female 23,720 13,833 18,831 18,061 13,274 17,354 15,974 18,798 a. Use a 0.01 significance level to test the claim that among couples, males speak fewer words in a day than females. In this example, uo is the mean value of the differences d for the population of all pairs of data, where each individual difference d is defined as the words spoken by the male minus words spoken by the female. What are the null and alternative hypotheses for the hypothesis test? Ho: Hd word(s) H1 : Hd word(s) (Type integers or decimals. Do not round.) Identify the test statistic. t=(Round to two decimal places as needed.) Identify the P-value. P-value = (Round to three decimal places as needed.) What is the conclusion based on the hypothesis test? Since the P-value is the significance level, the null hypothesis. There V sufficient evidence to support the claim that males speak fewer words in a day than females. b. Construct the confidence interval that could be used for the hypothesis test described in part (a). What feature of the confidence interval leads to the same conclusion reached in part (a)? The confidence interval is | word(s)