What is the probability that there will be between 34 and 46 left handed students in a group of 400?
To find the probability of there being between 34 and 46 left-handed students in a group of 400, we can use the binomial distribution formula.
The probability of getting exactly k successes in n trials is given by the formula:
P(x = k) = (n choose k) * p^k * (1-p)^(n-k)
Where:
n = number of trials or students in the group (400)
k = number of successes or left-handed students (34 to 46)
p = probability of success (assuming 10% of people are left-handed, p = 0.1)
To find the probability of there being between 34 and 46 left-handed students, we need to calculate the sum of individual probabilities for k = 34, 35, 36, ..., 46:
P(34 ≤ x ≤ 46) = P(34) + P(35) + P(36) + ... + P(46)
= Σ (n choose k) * p^k * (1-p)^(n-k) where k ranges from 34 to 46
Calculating this expression will give us the required probability.