Question

Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar. A medical center observed that about 60% of its morning appointments were with elderly patients. The table shows the results of a simulation used to represent the scenario. The numbers 0 to 5 represent appointments with elderly patients, and the numbers 6 to 9 represent appointments with other patients.

Answer 1

Answer:

1) 0.1504

2) 0.432

Step-by-step explanation:

1) The given information are;

The proportion of the morning appointments that are with elderly patients = 60%

The number of patients in the appointments  = 10 patients

The proportion of the morning appointments that are with non-elderly patients = 100 - 60 = 40%

The binomial probability distribution is given as follows;

$P(X = r) = \dbinom{n}{r}p^{r}\left (1-p \right )^{n-r}$

$P(X = 0) = \dbinom{10}{0}0.6^{0}\left (1-0.6 \right )^{10}$ = 0.000105

$P(X = 1) = \dbinom{10}{1}0.6^{1}\left (1-0.6 \right )^{9}$ = 0.0016

$P(X = 2) = \dbinom{10}{2}0.6^{2}\left (1-0.6 \right )^{8}$= 0.01062

$P(X = 3) = \dbinom{10}{3}0.6^{3}\left (1-0.6 \right )^{7}$= 0.0425

The probability that the first four patients are elderly is 0.000105 + 0.0016 + 0.1062 + 0.0425 = 0.1504

2) The probability that exactly 2 out of 3 morning patients are elderly patient is given as follows

$P(X = 2) = \dbinom{3}{2}0.6^{2}\left (1-0.6 \right )^{1}$= 0.432