Homework SourseIn studies for a medication 2 percent of patients gained wei
In studies for a medication, 2 percent of patients gained weight as a side effect. Suppose 698 patients are randomly selected. Use the normal approximation to the binomial to approximate the probability that (a) exactly 3 patients will gain weight as a side effect. (b) 3 or fewer patients will gain weight as a side effect. (c) 8 or more patients will gain weight as a side effect. (d) between 3 and 13 , inclusive, will gain weight as a side effect.
Solution
-MS Excel formula]:
| Given | |
| n= | 698 |
| Mean Proportion with side effect P0= | 0.02 |
| in number | 13.96 |
| So, sample standard error | |
| SE= | 0.005 |
| (a) exactly 3 patients will gain weight as a side effect | |
| Answer =0 | |
| Probability at any given fixed value is 0 for a continuous PDF | |
| (b) 3 or fewer patients will gain weight as a side effect. | |
| P= | 0.004 |
| Z-value | -2.963 |
| P(X<=3|Mean=14) = P(p<=0.0043|p0=.02) = P(Z<2.96)= | 0.15% |
| So answer is 0.15% | |
| (c) 8 or more patients will gain weight as a side effect. | |
| P= | 0.011 |
| Z-value | -1.611 |
| P(X<=3|Mean=14) = P(p<=0.0043|p0=.02) = P(Z<2.96)= | 94.64% |
| So answer is 94.64% | |
| (d) between 3 and 13 , inclusive, will gain weight as a side effect. | |
| P(3<=X<=13 | Mean=14) = P(X<=13 | Mean=14) - P(X<=3 | Mean=14) | |
| P(X<=13 | Mean=14) = | 39.76% |
| P(X<=3 | Mean=14) = | 0.15% |
| So, P(3<=X<=13 | Mean=14) = | 39.61% |
| So, answer is 39.61% |
