Question

An official from the securities commission estimates that 75% of all investment bankers have profited from the use of insider information. If 15 investment bankers are selected at random from the commission’s registry, find the probability that more than 12 have profited from insider information.

.236

.764

.654

.225

Answer 1

Solution

Given that ,

p = 75% = 0.75

1 - p = 1 - 0.75 = 0.25

n = 15

Using binomial probability formula ,

P(X = x) = ((n! / x! (n - x)!) * p^x * (1 - p)^{n - x}

P(X > 12) = P(X = 13) + P(X = 14) + P(X = 15)

= ((15! / 13! (2)!) * 0.75¹³ * (0.25)² + ((15! / 14! (1)!) * 0.75¹⁴ * (0.25)¹ + ((15! / 15! (0)!) * 0.75¹⁵ * (0.25)

= 0.236

Probability = 0.236