Answer:
The mean of x is close to 14.8.
The standard deviation of x is close to 3.78.
Step-by-step explanation:
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and each trial can only have two outcomes, with probabilities and
.
For an experiment with n repeated trials and a probability of success , we have that:
The mean is:
The standard deviation is:
In this problem
There are 400 employees, each with a probability of 3.7% of having food allergy. So . So:
The mean of x is close to 14.8.
The standard deviation of x is close to 3.78.