Given: Probability of getting a bad egg in a lot of 400 is 0.035.

To find: The number of bad eggs in the lot.

Solution:

Let X be the number of bad eggs in the lot of 400.

We know that the probability of getting a bad egg is 0.035. So, the probability of getting a good egg is 1 - 0.035 = 0.965.

Now, we can use the binomial distribution formula to find the probability of getting exactly x bad eggs in a lot of 400.

P(X = x) = (400Cx) (0.035)x (0.965)400-x

where, 400Cx = 400! / x!(400-x)!

We need to find the value of x for which P(X = x) is maximum.

We can use a calculator or a spreadsheet to calculate P(X = x) for different values of x and find the maximum value.

Alternatively, we can use the normal approximation to the binomial distribution when n is large and p is not too close to 0 or 1.

In this case, n = 400 and p = 0.035, so np = 14, which is not too small.

Using the normal approximation, we can find the mean and standard deviation of the number of bad eggs in a lot of 400.

Mean = np = 14

Standard deviation = sqrt(np(1-p)) = 3.28

Now, we can use the normal distribution to find the probability of getting x bad eggs.

P(X = x) ≈ N(14, 3.28)

We need to find the value of x for which P(X = x) is maximum.

The maximum value of the normal distribution occurs at the mean, which is 14.

Therefore, the number of bad eggs in the lot is 14.

Hence, option B is the correct answer.