You may use books, notes, and calculators, and work togetherin answering these questions.Suppose that a random sample ofn= 400 people in the U.S. shows thatX= 46 of them areleft-handed. Letpbe the actual proportion of left-handed people in the U.S

.1 What is the proportion (p) of left-handed people in the sample referred to above? (Write youranswer in decimal form, accurate to three decimal places.)

2. Suppose thatpis actually 0.1 (that is, 10% of the U.S. population is left-handed). What arethe mean (p) and the standard deviation (p) of the distribution of sample proportions in thiscase? (Write your answers in decimal form, withpaccurate to three decimal places.)

3. Which of the following is true about the probability that the sample proportion (p) is as calcu-lated in Question 1 (or is larger) if in factp= 0.1? (Circle the letter for the best answer. Youcan receive partial credit, here and in Question 5, for correctly presenting this probability interms ofZ, that is, asP(Z > Z0) orP(Z < Z0) for the right value ofZ0.)a) It is approximately 0.84b) It is approximately 0.34c) It is approximately 0.16d) It is no larger than 0.00024. Suppose now thatpis actually 0.2 (that is, 20% of the U.S. population is left-handed). What arethe mean (p) and the standard deviation (p) of the distribution of sample proportions underthis new assumption? (Again makepaccurate to three decimal places.)

5. Which of the following is true about the probability that the sample proportion (p) is as calcu-lated in Question 1 (or is smaller) if in factp= 0.2?a) It is approximately 0.84b) It is approximately 0.34c) It is approximately 0.16d) It is no larger than 0.