Toss 5 coins amd observe the number pf heads that will occur.Compute the mean,variance and standard deviation
To calculate the mean, variance, and standard deviation, we first need to determine all possible outcomes when tossing 5 coins. Since each coin can either land heads or tails, there are 2^5 = 32 possible outcomes.
Next, we will count the number of heads in each outcome and calculate the mean, variance, and standard deviation based on these values.
To make the calculation easier, we can use the binomial distribution formula:
Mean (µ) = n * p
Variance (σ^2) = n * p * (1 - p)
Standard Deviation (σ) = √(n * p * (1 - p))
Where:
- n is the number of trials (5 coin tosses)
- p is the probability of success (landing heads)
To find the mean, let's determine the probability of getting heads in a single coin toss. Since there are 2 equally likely outcomes (heads or tails), the probability of heads is 1/2.
Mean (µ) = 5 * (1/2) = 2.5
Next, let's calculate the variance and standard deviation. We'll use the same probability of success: p = 1/2.
Variance (σ^2) = 5 * (1/2) * (1 - 1/2) = 5 * (1/2) * (1/2) = 5/4 = 1.25
Standard Deviation (σ) = √(5 * (1/2) * (1 - 1/2)) = √(5 * (1/2) * (1/2)) = √(5/4) = √1.25 ≈ 1.12
So, the mean (µ) is 2.5, the variance (σ^2) is 1.25, and the standard deviation (σ) is approximately 1.12 when tossing 5 coins.