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.

May 19, 2026Mathematics

ScanSolve AI Answer

May 19, 2026

Answer

np$.

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

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Identify the distribution parameters. Let X be the number of times the coin lands on its tail.

Asked on May 19, 2026Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

ScanSolve AI AnswerAnswered on May 19, 2026

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=(3)/(5). The mean of a binomial distribution is = np. The variance of a binomial distribution is ^2 = np(1-p). Calculate the mean and variance: = 150 × (3)/(5) = 30 × 3 = 90 ^2 = 150 × (3)/(5) × (1 - (3)/(5)\