The random variable X has a binomial distribution with n= 10 and p= 0.5. Determine the following probabilities: (a) P(X=5), (b) P(X≤2), (c) P(X≥9), (d) P(3≤X<5)

Answer 1

TI calculators have a binompdf and binomcdf function to calculate these for you. pdf is used for calculating the probability of getting exactly some # of successes, eg P(X = 5). Binom cdf is used for calculating the probability of a range of outcomes, eg P(X ≤ 2). For P(X ≥ 9), calculate 1 - P(X ≤ 8). For P(3 ≤ X < 5), Do P(X ≤ 4) - P(X ≤ 2).

By hand, P(X = 5) = 10C5·(.5)⁵(.5)⁵