In: Statistics and Probability
Suppose we have a binomial experiment in which success is defined to be a particular quality or attribute that interests us. (a) Suppose n = 40 and p = 0.38. (For each answer, enter a number. Use 2 decimal places.) n·p = n·q = Can we approximate p̂ by a normal distribution? Why? (Fill in the blank. There are four answer blanks. A blank is represented by _____.) _____, p̂ _____ be approximated by a normal random variable because _____ _____. first blank Yes No second blank can cannot third blank n·p exceeds n·p does not exceed n·q exceeds n·q does not exceed both n·p and n·q exceed n·p and n·q do not exceed fourth blank (Enter an exact number.) What are the values of μp̂ and σp̂? (For each answer, enter a number. Use 3 decimal places.) μp̂ = mu sub p hat = 3.75 Incorrect: Your answer is incorrect. σp̂ = sigma sub p hat = 21.25 Incorrect: Your answer is incorrect. (b) Suppose n = 25 and p = 0.15. Can we safely approximate p̂ by a normal distribution? Why or why not? (Fill in the blank. There are four answer blanks. A blank is represented by _____.) _____, p̂ _____ be approximated by a normal random variable because _____ _____. first blank Yes No Correct: Your answer is correct. second blank can cannot Correct: Your answer is correct. third blank n·p exceeds n·p does not exceed n·q exceeds n·q does not exceed both n·p and n·q exceed n·p and n·q do not exceed Correct: Your answer is correct. fourth blank (Enter an exact number.) 5 Correct: Your answer is correct. (c) Suppose n = 43 and p = 0.31. (For each answer, enter a number. Use 2 decimal places.) n·p = n·q = Can we approximate p̂ by a normal distribution? Why? (Fill in the blank. There are four answer blanks. A blank is represented by _____.) _____, p̂ _____ be approximated by a normal random variable because _____ _____. first blank Yes No second blank can cannot third blank n·p exceeds n·p does not exceed n·q exceeds n·q does not exceed both n·p and n·q exceed n·p and n·q do not exceed fourth blank (Enter an exact number.) What are the values of μp̂ and σp̂? (For each answer, enter a number. Use 3 decimal places.) μp̂ = mu sub p hat = σp̂ = sigma sub p hat =
, be approximated by a normal random variable because
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, be approximated by a normal random variable because
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, be approximated by a normal random variable because