A coin is tossed 150 times. The probability of landing on tail is 3/5. Calculate the mean and variance of the number of tails.

Step 1: Identify the distribution parameters.
Let $X$ be the number of times the coin lands on its tail. This is a binomial distribution with $n=150$ trials and probability of success (landing on tail) $p=\frac{3}{5}$.
The mean of a binomial distribution is $\mu = np$.
The variance of a binomial distribution is $\sigma^2 = np(1-p)$.

Calculate the mean and variance:

$$\mu = 150 \times \frac{3}{5} = 30 \times 3 = 90$$ $$$$