8.0235% of the employees of the Acme Tire store are enrolled in a 401k at the store. If the company has 600 employees, what is the probability that less than 40 employees are entered in the 401k.
To find the probability that less than 40 employees are enrolled in the 401k, we can use the binomial probability formula.
The binomial probability formula is: P(x) = C(n, x) * p^x * (1-p)^(n-x)
Where:
- P(x) is the probability of having exactly x successes
- n is the number of trials
- x is the number of successes
- p is the probability of success in each trial.
In this case:
- n = 600 (number of employees)
- x < 40 (number of employees enrolled in the 401k)
- p = 0.080235 (probability of an employee being enrolled in the 401k, which is 8.0235% expressed as a decimal)
We want to find the probability that less than 40 employees are enrolled in the 401k. This is equivalent to finding the probability of having 0, 1, 2, ..., 39 employees enrolled.
P(x < 40) = P(x=0) + P(x=1) + P(x=2) + ... + P(x=39)
To calculate the individual probabilities, we can substitute the values into the binomial probability formula for each x and sum them up.
Once we have those probabilities, we can sum them together to find the total probability of having less than 40 employees enrolled in the 401k.