Question

A binomial probability experiment is conducted with the given parameters. Use technology to find the probability of x successes in the n independent trials of the experiment. Use the Tech Help button for further assistance. nequals9​, pequals0.35​, xless than4 Upper P left parenthesis Upper X less than 4 right parenthesisequals nothing ​(Round to four decimal places as​ needed.)

Answer 1

solution:-

given that n = 9 , p = 0.35

formula for binomial probability

P(X = x) = ncr * p^r * q^(n-r)

here we have to solve

P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)

= 9C0 * 0.35^0 * (1-0.35)^(9-0) + 9C1 * 0.35^1 * (1-0.35)^(9-1) + 9C2 * 0.35^2 * (1-0.35)^(9-2) + 9C3 * 0.35^3 * (1- 0.35)^(9-3)

= 9!/(0!(9−0)!) * 0.35^0 * (1-0.35)^(9-0) + 9!/(1!(9−1)!) * 0.35^1 * (1-0.35)^(9-1) + 9!/(2!(9−2)!) * 0.35^2 * (1-0.35)^(9-2) + 9!/(3!(9−3)!) * 0.35^3 * (1-0.35)^(9-3)

= 0.0207+0.1004+0.2162+0.2716

= 0.6089