Question

In a certain​ state, about 65​%of drivers who are arrested for driving while intoxicated​ (DWI) are convicted. Complete parts B & C below.

B. What is the probability that exactly 8 out of 12 independently selected drivers are​ convicted? The probability that exactly 88 out of 12 drivers are convicted is Answer ____.  

(Type an integer or decimal rounded to three decimal places as​ needed.)

C. What is the probability that 8 or few drivers are convicted? The probability that 8 or fewer drivers are convicted is Answer_____.  

(Type an integer or decimal rounded to three decimal places as​ needed.)

Answer 1

b)

Here, n = 12, p = 0.65, (1 - p) = 0.35 and x = 8
As per binomial distribution formula P(X = x) = nCx * p^x * (1 - p)^(n - x)

We need to calculate P(X = 8)
P(X = 8) = 12C8 * 0.65^8 * 0.35^4
P(X = 8) = 0.234

c)

Here, n = 12, p = 0.65, (1 - p) = 0.35 and x = 8
As per binomial distribution formula P(X = x) = nCx * p^x * (1 - p)^(n - x)

We need to calculate P(X <= 8).
P(X <= 8) = (12C0 * 0.65^0 * 0.35^12) + (12C1 * 0.65^1 * 0.35^11) + (12C2 * 0.65^2 * 0.35^10) + (12C3 * 0.65^3 * 0.35^9) + (12C4 * 0.65^4 * 0.35^8) + (12C5 * 0.65^5 * 0.35^7) + (12C6 * 0.65^6 * 0.35^6) + (12C7 * 0.65^7 * 0.35^5) + (12C8 * 0.65^8 * 0.35^4)
P(X <= 8) = 0 + 0.0001 + 0.0008 + 0.0048 + 0.0199 + 0.0591 + 0.1281 + 0.2039 + 0.2367
P(X <= 8) = 0.653