Question

The probablility that a randoomly slected teenager studied at least once during the week was only .52. Let x be the number of teenagers who studied at least once during the week. what is the probability that AT LEAST 5 of the students in your study group of 10 have studied in the last week

find P(x greater than or equal to 5)

round to 5 decimal places

Answer 1

Solution

Given that ,

p = 0.52

1 - p = 1 - 0.52 = 0.48

n = 10

Using binomial probability formula ,

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

P(X 5) = 1 - P(X < 5)

= 1 - [P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)]

= 1 - [(10! / 0! (10)!) * 0.52⁰ * (0.48)¹⁰ + (10! / 1! (9)!) * 0.52¹ * (0.48)⁹+

(10! / 2! (8)!) * 0.52² * (0.48)⁸ + (10! / 3! (7)!) * 0.52³ * (0.48)⁷+ (10! /4! (6)!) * 0.52⁴ * (0.48)⁶ ]

= 1 - 0.32882

= 0.67118

  

Probability = 0.67118