According to the national institute of allergy and infectious diseases about 3.7% of american adults have a food allergy. a large company plans a lunch reception for its 400 employees. assume that employees are independent. let the randome variable x be the number of company employeees who have a food allergy. the mean and standard deviation of the distribution of x are closest to

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.

d

step-by-step explanation:

answer:   x = 3 + √11     and     x = 3 - √11

step-by-step explanation:

x² - 6x + 9 = 11

(x - 3)² = 11

x - 3 = ±√11

    x = 3 ± √11

x = 3 + √11     and     x = 3 - √11