(c) What is the probability that at least two of your professors are extroverts? If there are six professors and we want to find the probability that at least two are extroverts, this means that exactly 2, 3, 4, 5 or 6 professors could be extroverts. So, r 2, 3, 4, 5 or 6. Recall the addition rule for probability where at least one of the specified events will occur. This allows us to write the probability as follows. P(r 2 2) = P(2) + P(3) + P(4) + P(5) + P(6) A portion of the binomial distribution table is displayed below. nr 0.01 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 6. 0 0.941 0.735 0.531 0.377 0.262 0.178 0.118 0.075 0.047 0.028 0.016 0.008 1 0.057 0.232 0.354 0.399 0.393 0.356 0.303 0.244 0.187 0.136 0.094 0.061 2 0.001 0.031 0.098 0.176 0.246 0.297 0.324 0.328 0.311 0.278 0.234 0.186 0.000 0.002 0.015 0.041 0.082 0.132 0.185 0.235 0.276 0.303 0.313 0.303 4 0.000 0.000 0.001 0.005 0.015 0.033 0.060 0.095 0.138 0.186 0.234 0.278 5 0.000 0.000 0.000 0.000 0.002 0.004 0.010 0.020 0.037 0.061 0.094 0.136 6 0.000 0.000 0.000 0.000 0.000 0.000 0.001 0.002 0.004 0.008 0.016 0.028 Use the above table to find the P(r) values for r 2, 3, 4, 5 or 6 for n= 6 and p 0.45. (Round your answers to three decimal places.) P(r) 0.001 0.000 2. 3. 0.000 0.061 0.008 4.
(c) What is the probability that at least two of your professors are extroverts? If there are six professors and we want to find the probability that at least two are extroverts, this means that exactly 2, 3, 4, 5 or 6 professors could be extroverts. So, r 2, 3, 4, 5 or 6. Recall the addition rule for probability where at least one of the specified events will occur. This allows us to write the probability as follows. P(r 2 2) = P(2) + P(3) + P(4) + P(5) + P(6) A portion of the binomial distribution table is displayed below. nr 0.01 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 6. 0 0.941 0.735 0.531 0.377 0.262 0.178 0.118 0.075 0.047 0.028 0.016 0.008 1 0.057 0.232 0.354 0.399 0.393 0.356 0.303 0.244 0.187 0.136 0.094 0.061 2 0.001 0.031 0.098 0.176 0.246 0.297 0.324 0.328 0.311 0.278 0.234 0.186 0.000 0.002 0.015 0.041 0.082 0.132 0.185 0.235 0.276 0.303 0.313 0.303 4 0.000 0.000 0.001 0.005 0.015 0.033 0.060 0.095 0.138 0.186 0.234 0.278 5 0.000 0.000 0.000 0.000 0.002 0.004 0.010 0.020 0.037 0.061 0.094 0.136 6 0.000 0.000 0.000 0.000 0.000 0.000 0.001 0.002 0.004 0.008 0.016 0.028 Use the above table to find the P(r) values for r 2, 3, 4, 5 or 6 for n= 6 and p 0.45. (Round your answers to three decimal places.) P(r) 0.001 0.000 2. 3. 0.000 0.061 0.008 4.
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Transcribed Image Text:(c) What is the probability that at least two of your professors are extroverts?
If there are six professors and we want to find the probability that at least two are extroverts, this means that
exactly 2, 3, 4, 5 or 6 professors could be extroverts. So, r = 2, 3, 4, 5 or 6.
Recall the addition rule for probability where at least one of the specified events will occur. This allows us to
write the probability as follows.
P(r 2 2) = P(2) + P(3) + P(4) + P(5) + P(6)
%3!
A portion of the binomial distribution table is displayed below.
n
0.01
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0.45
0.50
0.55
6.
0.941 0.735 0.531 0.377 0.262 0.178 0.118 0.075 0.047 0.028 0.016 0.008
0.057 0.232 0.354 0.399 0.393 0.356 0.303 0.244 0.187 0.136 0.094 0.061
2 0.001 0.031 0.098 0.176 0.246 0.297 0.324 0.328 0.311 0.278 0.234 0.186
3 0.000 0.002. 0.015 0.041 0.082 0.132 0.185 0.235 0.276 0.303 0.313 0.303
4 0.000 0.000 0.001 0.005 0.015 0.033 0.060 0.095 0.138 0.186 0.234 0.278
5 0.000 0.000 0.000 0.000 0.002 0.004 0.010 0.020 0.037 0.061 0.094 0.136
6 0.000 0.000 0.000 0.000 0.000 0.000 0.001 0.002 0.004 0.008 0.016 0.028
Use the above table to find the P(r) values for r 2, 3, 4, 5 or 6 for n 6 and p = 0.45. (Round your answers
to three decimal places.)
P(r)
0.001
3.
0.000
0.000
0.061
0.008
4
5.
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