13 A random number generator picks a number from 19 to 37 in a uniform manner. Round answers to 4 decimal places when possible. a. The mean of this distribution is 28 b. The standard deviation is 5.1962 c. The probability that the number will be exactly 33 is P(x = 33) = 0 d. The probability that the number will be between 25 and 36 is P(25 29) = 0.5556 X f. P(x > 23 | x The mean height of an adult giraffe is 18 feet. Suppose that the distribution is normally distributed with standard deviation 0.9 feet. Let X be the height of a randomly...r selected adult giraffe. Round all answers to 4 decimal places where possible. a. What is the distribution of X? I ~ Nfl '13 I, [1.81 X] of b. What is the median giraffe height? [ '13 Jl ft. of c. What is the l-score for a giraffe that is 19.5 foot tall?| 1.656? I of d. What is the probability that a randomly.r selected giraffe will be shorter than 1?.2 feet tall? [1.8133 X e. What is the probability that a randomly.r selected giraffe will be between 1?.1 and 11? feet tall? 0.2?95 3-: f. The ?th percentile for the height of giraffes is ft. Suppose that the distance of fl}...r balls hit to the outfield {in baseball] is normally distributed with a mean of 259 feet and a standard deviation of 44 feet. Let I be the distance in feet for a fly...r ball. a. What is the distribution [if it? it ~ iii 259 H 44 J] a\" as b. Find the probability that a randomly.r hit fly,r ball travels less than 121 feet. Round to 4 decimal places. 0.19489 X c. Find the 85th percentile for the distribution of distance of fly balls. Round to 2 decimal places. 3% X feet I24 " The average student Loan debt for college graduates is $25,950. Suppose that that distribution is normal and that the standard deviation is $13,550. Let X = the student loan debt of a randomly selected college graduate. Round all probabilities to 4 decimal places and all dollar answers to the nearest dollar. a. What is the distribution of X? X ~ NI[| 25950 J, 106m] 3-: ]. o\" b Find the probability,r that the college graduate has between 511100 and 534,400 in student loan debt. [ [1.4333 ' o" c. The middle 1033 of college graduates' Loan debt lies between what two numbers? Low:$ 133143332 x High: 5 321353323 3: I25 ' 4: > On the planet of Mercury, 4-year-olds average 2.9 hours a day unsupervised. Most of the unsupervised children live in rural areas, considered safe. Suppose that the standard deviation is 1.5 hours and the amount of time spent alone is normally distributed. We randomly survey one Mercurian 4-yearold living in a rural area. We are interested in the amount of time X the child spends alone per day. (Source: San Jose Mercury News] Round all answers to 4 decimal places where possible. a. What is the distribution of X? X ~ N{ 2.9 J b. Find the probability that the child spends less than 2.3 hours per day unsupervised. 0.34 X c. 1What percent of the children spend over 2 hours per day unsupervised. 0.23 X 5:\" [Round to 2 decimal places} d. 81 1:} of all children spend at least hOW many hours per day unsupervised? 4.09 X hours. ,14 )Ho&quot