Hospital records show that of patients suffering from a certain disease, 25% die of it. (i) What is the probability that of 6 randomly selected patients, 4 will recover? [3 marks] (ii) What is the most probable number of recoveries out of 6 randomly selected patients? [2 marks] Page 3 of 5 (iii) Compute and plot a bar graph of the probability distribution of recoveries out of 6 randomly selected patients. [5 marks] (iv) Plot the distribution function of the number of recoveries out of 6 randomly selected patients.
Let "X=" the number of recovered patients: "X\\sim Bin(n, p)."
Given "n=6, q=0.25, p=1-q=1-0.25=0.75."
(i)
"=0.2966"
(ii)
The mode is an integer "M" that satisfies
"(6+1)\\cdot0.75-1\\leq M<(6+1)\\cdot0.75"
"4.25\\leq M<5.25"
"M=5"
"P(X=5)=\\dbinom{6}{5}(0.75)^5(0.25)^{6-5}"
"=0.35595703125"
The most probable number of recoveries out of 6 randomly selected patients is "5" patients.
(iii)
"=0.0002"
"=0.0044"
"=0.0330"
"=0.1318"
"=0.2966"
"=0.3560"
"=0.1780"
(iv)
Comments
Leave a comment