Question

Of those mountain climbers who attempt Mt. McKinley, only 65% reach the summit. In random sample of 11 mountain climbers who attempt to climb Mt. KcKinley, what is the probability of 11 mountain climbers reaching the summit? Round to 4 decimal values

Answer 1

Probability that all 11 sampled mountain climbers make it to the top of Mt. McKinley = 0.088

Explanation:

This is a binomial distribution problem

Binomial distribution function is represented by

P(X = x) = ⁿCₓ pˣ qⁿ⁻ˣ

n = total number of sample spaces = number of mountain climbers sampled = 11

x = Number of successes required = 11

p = probability of success = Probability that one mountain climbers makes it the top of Mt. McKinley = 0.65

q = probability of failure = 1 - p = 0.35

P(X = 11) = ¹¹C₁₁ (0.65)¹¹ (0.35)¹¹⁻¹¹

P(X=11) = 0.00875078317 = 0.0088 to 4 d.p

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