6. A nutraceu suppl independent laboratory examines 30 supplement. What is the p

Question

6. A nutraceu suppl independent laboratory examines 30 supplement. What is the probability of the following events? tical company has introduced a new weight-loss product and states that the ement causes negative side effects in only 5% of patients. To confirm this statement, an randomly selected users who have consumed the a. Two of the 30 users experienced negative side effects (3 points) %;:0666? b. More than three of the 30 users experienced negative side effects (3 points) What is the mean number of users that the laboratory should expect to experience negative side effects if they examine 30 users at random? 12 points) c. d. What is the standard deviation for the distribution of 30 randomly selected users whe the probability of negative side effects is.05? (2 points) supplement, and 9 people experienced side effects, what conclusion would you draw about the nutraceutical company's claim that the supplement causes negative side effects in only 5 out of 100 users? Use probability to explain. (5 points) e. If the independent laboratory chooses 30 people at random who have consumed the

Explanation / Answer

Here X is the random variable denoting the number of users affected by the supplements with negatives side affects. Since a sample of 30 has been selected Here X follows binomial distribution with X~Binomial(30,0.05) 1)to calculate the probabilty that 2of the 30 users have been affected by nagativeside affects. the binomial distributin is given as Bin(n,p)=nCx*px *(1-p)n-x. therefore P(X=2)=30C2*(0.05)2*(1-0.05)30-2=0.2586. 2)to calculate the probability of more than 3 P(X>3)=1-P(X

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