1 2 4 6 8 9 Read the directions carefully. Show ALL OF YOUR WORK!! Label your parts as you work. Write any commands you use on the calculator. 1. (3 pts) An interesting phenomenon is that the first digits of numbers in legitimate records (tax returns financial statements, invoices, for example) often follow a discrete distribution known as Benford's Law. The distribution appears below. First digit 3 7 Proportion 0.301 0.176 0.125 0.097 0.079 0.067 0.058 0.051 0.046 Fake records typically have fewer first digits of 1. 2. or 3. What is the approximate probability. if Benford's Law holds, that among 1000 randomly chosen invoices there are at most 560 in amounts with first digit 1. 2. or 3? (Interesting trivia: The IRS uses Benford's Law as part of their audit criterion 2. (2 pts each) According to genetic theory, the blossom color in the second generation of a certain cross of sweet peas should be red or white with the probability of a plant having red blossoms being The blossom colors of separate plants are independent (a) Find the probability that exactly 9 out of 12 of these plants have red blossom (b) If 120 plants are grown from seeds, find the probability of having at least 80 red-blossomed plants. 3. (3 pts) History has shown that ex of registered voters in Jefferson County support a state constitution amendment to allow casino gambling in Kentucky Suppose the Courier Journal selects a random sample of 200 registered voters in Jefferson County annaks if they tappott a state constitutional amendment to allow casino gambling in Kentucky. Approximate the probability that fewer than half of the respondents in the poll support a state constitutional amendment to allow casino gambling it Kettucky 2021SP BU-299-01: R... (8) Sun 8:19 PM 1 2 4 6 8 9 Read the directions carefully. Show ALL OF YOUR WORK!! Label your parts as you work. Write any commands you use on the calculator. 1. (3 pts) An interesting phenomenon is that the first digits of numbers in legitimate records (tax returns financial statements, invoices, for example) often follow a discrete distribution known as Benford's Law. The distribution appears below. First digit 3 7 Proportion 0.301 0.176 0.125 0.097 0.079 0.067 0.058 0.051 0.046 Fake records typically have fewer first digits of 1. 2. or 3. What is the approximate probability. if Benford's Law holds, that among 1000 randomly chosen invoices there are at most 560 in amounts with first digit 1. 2. or 3? (Interesting trivia: The IRS uses Benford's Law as part of their audit criterion 2. (2 pts each) According to genetic theory, the blossom color in the second generation of a certain cross of sweet peas should be red or white with the probability of a plant having red blossoms being The blossom colors of separate plants are independent (a) Find the probability that exactly 9 out of 12 of these plants have red blossom (b) If 120 plants are grown from seeds, find the probability of having at least 80 red-blossomed plants. 3. (3 pts) History has shown that ex of registered voters in Jefferson County support a state constitution amendment to allow casino gambling in Kentucky Suppose the Courier Journal selects a random sample of 200 registered voters in Jefferson County annaks if they tappott a state constitutional amendment to allow casino gambling in Kentucky. Approximate the probability that fewer than half of the respondents in the poll support a state constitutional amendment to allow casino gambling it Kettucky 2021SP BU-299-01: R... (8) Sun 8:19 PM