Complete Question
Determine the probability P(1 or fewer) for a binomial experiment with n = 16 trials and the success probability p = 0.2. Then find the mean, variance, and standard deviation
Answer:
The probability is 
The mean is 
The variance is 
The standard deviation is 
Step-by-step explanation:
From the question we are told that
The probability of success is p = 0.2
The sample size is n = 16
Generally this experiment follows a binomial distribution
i.e
and the probability distribution function for binomial distribution is
Here C stands for combination hence we are going to be making use of the combination function in our calculators
Generally the the probability P(1 or fewer) is mathematically represented as

=> ![P(X \le 1 ) = [^{15}C_0 * (0.2)^0 * (1- 0.2)^{15-0}] + [^{15}C_1 * (0.20)^1 * (1- 0.20)^{15-1} ]](https://tex.z-dn.net/?f=P%28X%20%5Cle%201%20%29%20%3D%20%20%5B%5E%7B15%7DC_0%20%2A%20%20%280.2%29%5E0%20%2A%20%20%281-%200.2%29%5E%7B15-0%7D%5D%20%2B%20%5B%5E%7B15%7DC_1%20%2A%20%20%280.20%29%5E1%20%2A%20%20%281-%200.20%29%5E%7B15-1%7D%20%5D)
=> ![P(X \le 1 ) = [1 * 1* 0.0352 ] + [15 * 0.20 * 0.0439]](https://tex.z-dn.net/?f=P%28X%20%5Cle%201%20%29%20%3D%20%20%5B1%20%2A%20%201%2A%20%200.0352%20%5D%20%2B%20%5B15%20%2A%20%200.20%20%2A%20%200.0439%5D)
=> 
Generally the mean for this experiment is mathematically represented as

=> 
=> 
Generally the variance is mathematically represented as

=> 
=> 
Generally the standard deviation is mathematically represented as

=> 