SOLUTION: Hi tutors, I need help with the following question: A distinguishing characteristic of entrepreneurs is their willingness to take risks. R.H. Brockhaus (Academy of Manag

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Question 397986: Hi tutors,
I need help with the following question:
A distinguishing characteristic of entrepreneurs is
their willingness to take risks. R.H. Brockhaus (Academy of
Management Journal, Sept. 1980) used a choice dilemma questionaire
(CDQ) to measure the risk-taking propensities of successful
entrepreneurs (lower scores associated with a higher tendancy
for risk taking). The CDQ scores are normally distributed
with a mean of 73 and a standard deviation of 9.
If four entrepreneurs are randomly selected, what is the
probability that at least two of them will score more than 74 on
the CDQ?
I tried solving it by the following formula: p(x>=74), then finding the probability using area under the normal curve but I don't know what to do with the information saying at least 2 out of 4 entrepreneurs. I will be really grateful for your help, thanks!
Answer by robertb(5830) (Show Source):
You can put this solution on YOUR website!
Assuming that the probability of any ONE entrepreneur getting a score X is normally distributed, the probability of scoring is .
Let
, and
.
COMPUTE for these two values and .
From here on the binomial distribution takes over.
Thus the probability that at least two of them will score more than 74 on
the CDQ is .
Compute for this value,and that's it.