Question: Health status of UNCC students was investigated in the research study. The distribution of fasting glucose (FG) was approximately normally distributed with mean 97 and standard deviation of 10. During 12 days, a sample of fifty students was selected. What is the probability that at least 6 students have FG < 87? Selected values of CDF (cumulative probabilities) for Binomial distributions are below. Please, justify your answer.

Binomial Cumulative Probabilities

p n k P(X≤k)__

0.16 6 2 0.94396

0.16 6 3 0.99252

0.16 6 4 0.99945

0.16 6 5 0.99998

0.16 12 2 0.70100

0.16 12 3 0.88863

0.16 12 4 0.96904

0.16 12 5 0.99355

0.16 12 6 0.99900

0.16 12 7 0.99988

0.16 50 2 0.00900

0.16 50 3 0.03117

0.16 50 4 0.08078

0.16 50 5 0.16773

0.16 50 6 0.29194

0.16 50 7 0.44065

0.68 6 2 0.08749

0.68 6 3 0.29356

0.68 6 4 0.62198

0.68 6 5 0.90113

0.68 12 2 0.00037

0.68 12 3 0.00281

0.68 12 4 0.01445

0.68 12 5 0.05401

0.68 12 6 0.15210

0.68 12 7 0.33077

0.68 50 24 0.00263

0.68 50 25 0.00612

0.68 50 26 0.01326

0.84 6 2 0.00748

0.84 6 3 0.05604

0.84 6 4 0.24722

0.84 6 5 0.64870

0.84 12 3 0.00001

0.84 12 4 0.00012

0.84 12 5 0.00100

0.84 12 6 0.00645

0.84 12 7 0.03096