According to the recent report,scientists in New England say they have identified a set of genetic variants that predicts extreme longevity with 77% accuracy.Assume 150 patients decide to get their genome sequenced.If the claim by scientists is accurate,what is the probability that fewer than 70% of the patientswill get a correct diagnosis for extreme longevity?A.0.0207
A) 0.1422
B) 0.0722
C) 0.2214

Question

Quizplus · Accepted Answer

We can use the binomial distribution to calculate the probability of fewer than 70% of the patients getting a correct diagnosis. Let X be the number of patients who get a correct diagnosis, then X follows a binomial distribution with n=150 and p=0.77.

P(X<0.7*150) = P(X<105)

Using the normal approximation to binomial distribution with mean = np = 150*0.77 = 115.5 and standard deviation = sqrt(npq) = 5.91, we have:

Z = (105-115.5)/5.91 = -1.78

Using the standard normal distribution table or calculator, we can find P(Z<-1.78) = 0.0384.

Therefore, the probability of fewer than 70% of the patients getting a correct diagnosis is 0.0384, which is closest to 0.0207 among the given options.

According to the Recent Report,scientists in New England Say They