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Assume that The amounts of weight That male college students gain during their freshman year are normally distlibuted with a mean of u =12 kg and a standard deviation olo=5.6 kg. Complete parts {a} Through (c) below. a. It 1 male college student is randomly selected. nd the probability That he gains between [1 kg and 3 kg during freshman year. The probability is (Round to four decimal places as needed.) b. If 25 male college students are randomly selected, nd the probability That their mean weight gain during freshman year is between 0 kg and 3 kg. The probability is (Round to four decimal places as needed.) {2. Why can The normal distribution be used in part [b], even Though the sample size does not exceed 30? O A. Since the original population has a normal distribution, The distribution of sample means is a normal distribution for any sample size. 0 B. Since the distribution is of individuals, not sample means, the distribution is a normal distribution for any sample size. 0 C. Since the weight gain exceeds 3D, the distribution of sample means is a normal distribution for any sample size. 0 D. Since the distribution is of sample means, not individuals, the distribution is a normal distribution tor any sample size. The sample space listing the eight simple events that are possible when a couple has three children is {bbb. bbg. bgb. bgg. gbb. gbg. ggb. ggg}. Alter identifying the sample space for a couple having tour children, nd the probability of getting tour girls and no boys. Identity.r the sample space for a couple having four children. {D} (Use a comma to separate answers as needed.) Find the probability of getting four girls and no boys. E (Type an integer or a decimal. Do not round.) Find the area of the shaded region. The graph to the right depicts IQ scores of adults, and those scores are normally distributed with a mean of 100 and a standard deviation of 15. 104 128 The area of the shaded region is . (Round to four decimal places as needed.)Here are summary statistics for randomly selected weights of newborn girls: n = 36, x = 3211.1 g, s=689.4 g. Use a confidence level of 99% to complete parts (a) through (d) below. a. Identify the critical value to/2 used for finding the margin of error. to /2 = (Round to two decimal places as needed.) b. Find the margin of error. E = 9 (Round to one decimal place as needed.) c. Find the confidence interval estimate of p. (Round to one decimal place as needed.) d. Write a brief statement that interprets the confidence interval. Choose the correct answer below. O A. There is a 99% chance that the true value of the population mean weight of newborn girls will fall between the lower bound and the upper bound. O B. One has 99% confidence that the sample mean weight of newborn girls is equal to the population mean weight of newborn girls. O C. One has 99% confidence that the interval from the lower bound to the upper bound contains the true value of the population mean weight of newborn girls. O D. Approximately 99% of sample mean weights of newborn girls will fall between the lower bound and the upper bound.Find the (a) mean, (b) median, {c} mode, and (d) midrange for the given sample data. An experiment was conducted to determine whether a deciency of carbon dioxide in the soil aects the phenotype of peas. Listed below are the phenotype codes where '1 =smooih-yellow, 2=smooth-green, 3=wrinkled-ye||ow, and 4 =wrinkled-green. Do the results make sense? 2 1 'l 2 3 2 3 1 3 2 4 2 2 '1 g E) (a) The mean phenotype code is D. (Round to the nearest tenth as needed.) (b) The median phenotype code is (Type an integer or a decimal} (c) Select the correct choice below and fill in any answer boxes within your choice. 0 A- The mode phenotype code is D. (Use a comma to separate answers as needed.) 0 B. There is no mode. (d) The midrange ofthe phenotype codes is E. (Type an integer or a decimal.) Do the measures of center make sense? 0 A. Only the mean, median, and midrange make sense since the data is nominal. O B. Only the mean, median, and mode make sense since the data is numerical. O C. All the measures oi center make sense since the data is numerical. O D. Only the mode makes sense since the data is nominal