a) Explain the reason to use binomial formula instead of using normal approximation to obtain the required probability. b) Explain the reason for the authors of the study can propose that someone who scores 42 or less on the MENT exam is faking the test.

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a) Explain the reason to use binomial formula instead of using normal approximation to obtain the required probability.  b) Explain the reason for the authors of the study can propose that someone who scores 42 or less on the MENT exam is faking the test.

rogreenhoxa8 · Accepted Answer

a) It is given that the random variable x follows binomial distribution with n=60 and p=0.96. The random variable x is defined as number of correct responses on the MENT test for a patient who is trying to fake the test. Also, exact binomial probability of a score of 42 or less for someone who is not faking the test is p(x≤42)=0.000000000013. Conditions for binomial to follow normal distribution (approximately): np≥10 n(1−p)≥10 Substitute n=60 and p=0.96. np=(60)(0.96) =57.6 &amp;gt;10 n(1−p)=(60)(1−0.96) =(60)(0.04) =2.4 &amp;lt;10 Thus, the condition n(1−p)≥10 is not satisfied. Hence, the distribution of x cannot be approximated to normal. Hence, binomial formula is used to approximate when p=0.96. b) The exact binomial probability of a score of 42 or less for someone who is not faking the test is p(x≤42)=0.000000000013. Since the probability is less the event of a score of 42 or less is unlikely to happen. Therefore, the authors of the study can propose that someone who scores 42 or less on the MENT exam is faking the test.

a) Explain the reason to use binomial formula instead of

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