In a survey of college graduates, 61% reported that they entered a profession closely related to their college major. If 8 college graduates are randomly selected, use the binomial distribution to find the probability of each item. a) Getting exactly 3(x=3) that entered a profession closely related to their major. b) Getting 3 or fewer (x≤3) that entered a profession closely related to their major. c) Getting at least one (x≥1) that entered a profession closely related to their major.

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In a survey of college graduates, 61% reported that they entered a profession closely related to their college major. If 8 college graduates are randomly selected, use the binomial distribution to find the probability of each item.   a) Getting exactly 3(x=3) that entered a profession closely related to their major.   b) Getting 3 or fewer (x≤3) that entered a profession closely related to their major.   c) Getting at least one (x≥1) that entered a profession closely related to their major.

Virginia Palmer · Accepted Answer

Introduction  As per Bartleby guideline if more than three subparts is asked only first three to be answered kindly upload the another one separately.  To find the probability of each item:  a) Getting exactly 3(x=3) that entered a profession closely related to their major.  b) Getting 3 or fewer (x≤3) that entered a profession closely related to their major.  c) Getting at least one (x≥1) that entered a profession closely related to their major.  Step 2  Given data:  In a survey of college graduates, 61% reported that they entered a profession closely related to their college major.  If 8 college graduates are randomly selected.  n=8  p=0.61  q=0.39  Use the binomial distribution to find the probabilities given below:  a) The probability of Getting exactly 3 that entered a proffession closely related to their major:  P(X=x)=(nx)(p)x(q)n−x  P(X=3)=(83)(0.61)3(0.39)5  =56(0.227)(0.009)  =0.115  Step 3  b) The probability of Getting 3 or fewer that entered a proffession closely related to their major:  P(X≤3)=P(X=0)+P(X=1)+P(X=2)+P(X=3)  =(80)(0.61)0(0.39)8+(81)(0.61)1(0.39)7+(82)(0.61)2(0.39)6+(83)(0.61)3(0.39)5  =0.0005+0.0067+0.0367+0.115  =0.159  c) The probability of Getting at least one that entered a profession closely related to their major:  P(X≥1)=1−P(X≤1)  =1−(P(X=0)+P(X=1))  =1−((80)(0.61)0(0.39)8+(81)(0.61)1(0.39)7)  =1−(0.0005+0.0067)  =0.9928  Conclusion  a) The probability of Getting exactly 3 that entered a profession closely related to their major is 0.115  b) The probability of Getting 3 or fewer that entered a profession closely related to their major is 0.159  c) The probability of Getting at least one that entered a profession closely related to their major is 0.9928

Juan Spiller · Accepted Answer

Step 1  a) P(X=x)=(nx)(p)x(q)n−x  P(X=3)=(83)(0.61)3(0.39)5  56(0.227)(0.009)  =0.115  Step 2  b) P(X≤3)=P(X=0)+P(X=1)+P(X=2)+P(X=3)  =(80)(0.61)0(0.39)8+(81)(0.61)1(0.39)7+(82)(0.61)2(0.39)6  +(83)(0.61)3(0.39)5  =0.0005+0.0067+0.0367+0.115  =0.159  Step 3  c) P(X≥1)=1−P(X≤1)  =1−(P(X=0)+P(X=1))  =((80)(0.61)0(0.39)8+(81)(0.61)190.39)7)  =1−(0.0005+0.0067)  =0.9928

In a survey of college graduates, 61% reported that they ent

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