T2E - Please provide answers first - followed by (brief explanation)

PART1

When Mendel experimented with crossing different types of peas, he noted both the color (green or yellow) and the shape (round or wrinkled) of the peas produced. The table below gives the predicted percentage of each type according to Mendelian genetics. Green Yellow Round 0.1875 0.5625 Wrinkled 0.0625 0.1875 (a) If one pea is drawn at random from the peas produced, what is the probability it is round? (b) If a simple random sample of 20 peas is drawn from those produced, what is the expected number of round peas? (c) If a simple random sample of 20 peas is drawn from those produced, what is the standard deviation of the number of round peas? (Round your answer to two decimal places.)The table below shows a random sample of musicians and how they learned to play their instruments. Gender Self-taught Studied in School Private Instruction Total Female 11 34 23 68 Male 16 22 24 62 Total 27 56 47 130 Find P(musician is a male AND had private instruction). (Enter your probability as a fraction.) P(musician is a male AND had private instruction) =A ballet instructor is interested in knowing what percent of each year's class will continue on to the next, so that she can plan what classes to offer. Over the years, she has established the following probability distribution. . Let X = the number of years a student will study ballet with the teacher. . Let P(x) = the probability that a student will study ballet x years. Complete the table below using the data provided. (Enter exact numbers as integers, fractions, or decimals.) X P(x) x*P(x) 1 0.05 2 0.10 3 0.20 4 5 0.30 6 0.10 7 0.05Identify the mistake in the probability distribution table. X P(x) x*P(x) 1 0.15 0.15 2 0.25 0.40 3 0.25 0.65 4 0.20 0.85 5 0.15 1 O The values of x*P(x) are not correct. O The values of P(x) do not sum to one. O The values of P(x) are not between zero and one. O The values of x*P(x) do not sum to one. O The values of x are not correct