Psychologist Michael Cunningham conducted a survey of university women to see wh

Question

Psychologist Michael Cunningham conducted a survey of university women to see whether, upon graduation, they would prefer to marry a high school teacher who has short workdays, summers off, and spare energy to help raise children, or a surgeon who earns eight times as much but works brutal hours. He found that 75% of the university women said they would choose the teacher. [Source: Alex Williams, "Putting Money on the Table, " The New York Times, September 23, 2007.] Select the appropriate distribution in the Distributions tool to help answer the questions that follow. Nate is single and completing the last year of his surgical residency at Brown Medical School. He decides that it's time to get married and embarks on a mission to find his soul mate. His strategy is to select 25 female university graduates randomly and take each prospect on a date sometime during the next 2 months. Let X denote the number of Nate's dates who prefer surgeons. The probability that exactly six of Nate's dates are women who prefer surgeons is __. The probability that at least 10 of Nate's dates are women who prefer surgeons is __. The expected value of X is __, and the standard deviation of X is __.

Explanation / Answer

n = 20

p = 1- 0.75 = 0.25

A) P (x =6 ) = 20C6 * (0.25)6 * (1 - 0.25)20 - 6

. = 0.17

B) P(x > = 10) = P (x = 10) + P (x = 11) + P (x = 12) + P( x = 13) + P (x = 14) + P (x = 15) + P (x = 16) + P (x = 17) + P (x = 18) + P (x = 19) + P (x = 20)

= 20C10 * (0.25)10 * (0.75)10 + 20C11 * (0.25)11 * (0.75)9 + 20C12 * (0.25)12 * (0.75)8 + 20C13 * (0.25)13 * (0.75)7 + 20C120C14 * (0.25)14 * (0.75)6 + 20C15 * (0.25)15 * (0.75)5 + 20C16 * (0.25)16 * (0.75)4 + 20C17 * (0.25)17 * (0.75)3 + 20C18 * (0.25)18 * (0.75)2 + 20C19 * (0.25)19 * (0.75)1 + 20C20 * (0.25)20 * (0.75)0 = 0.014

C) expected value of x = n * p = 20 * 0.25 = 5

Standard deviation = sqrt(n * p * (1 - p))

= Sqrt (20 * 0.25 * 0.75)

= 1.94

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