Math / Data & Statistics

QuestionA fair coin is tossed six times. Find the mean, variance and standard deviations of number of heads obtained. (Round the answers upto 3 decimal places)
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Studdy Solution

STEP 1

1. The coin is fair, meaning the probability of heads (success) is $p = 0.5$ .
2. The number of trials (coin tosses) is $n = 6$ .
3. The distribution of the number of heads follows a binomial distribution.

STEP 2

1. Calculate the mean of the binomial distribution.
2. Calculate the variance of the binomial distribution.
3. Calculate the standard deviation of the binomial distribution.

STEP 3

The mean $\mu$ of a binomial distribution is given by the formula:
$\mu = n \times p$
Substitute $n = 6$ and $p = 0.5$ :
$\mu = 6 \times 0.5 = 3$

STEP 4

The variance $\sigma^2$ of a binomial distribution is given by the formula:
$\sigma^2 = n \times p \times (1 - p)$
Substitute $n = 6$ and $p = 0.5$ :
$\sigma^2 = 6 \times 0.5 \times (1 - 0.5) = 6 \times 0.5 \times 0.5 = 1.5$

STEP 5

The standard deviation $\sigma$ is the square root of the variance:
$\sigma = \sqrt{\sigma^2} = \sqrt{1.5} \approx 1.225$
The mean is:
$\boxed{3}$
The variance is:
$\boxed{1.5}$
The standard deviation is:
$\boxed{1.225}$

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QuestionA fair coin is tossed six times. Find the mean, variance and standard deviations of number of heads obtained. (Round the answers upto 3 decimal places)
Click here to enter an

Studdy Solution

STEP 1

1. The coin is fair, meaning the probability of heads (success) is $p = 0.5$ .
2. The number of trials (coin tosses) is $n = 6$ .
3. The distribution of the number of heads follows a binomial distribution.

STEP 2

1. Calculate the mean of the binomial distribution.
2. Calculate the variance of the binomial distribution.
3. Calculate the standard deviation of the binomial distribution.

STEP 3

The mean $\mu$ of a binomial distribution is given by the formula:
$\mu = n \times p$
Substitute $n = 6$ and $p = 0.5$ :
$\mu = 6 \times 0.5 = 3$

STEP 4

The variance $\sigma^2$ of a binomial distribution is given by the formula:
$\sigma^2 = n \times p \times (1 - p)$
Substitute $n = 6$ and $p = 0.5$ :
$\sigma^2 = 6 \times 0.5 \times (1 - 0.5) = 6 \times 0.5 \times 0.5 = 1.5$

STEP 5

The standard deviation $\sigma$ is the square root of the variance:
$\sigma = \sqrt{\sigma^2} = \sqrt{1.5} \approx 1.225$
The mean is:
$\boxed{3}$
The variance is:
$\boxed{1.5}$
The standard deviation is:
$\boxed{1.225}$

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QuestionA fair coin is tossed six times. Find the mean, variance and standard deviations of number of heads obtained. (Round the answers upto 3 decimal places)Click here to enter an

Studdy Solution

STEP 1

1. The coin is fair, meaning the probability of heads (success) is p=0.5 p = 0.5 p=0.5.2. The number of trials (coin tosses) is n=6 n = 6 n=6.3. The distribution of the number of heads follows a binomial distribution.

STEP 2

1. Calculate the mean of the binomial distribution.2. Calculate the variance of the binomial distribution.3. Calculate the standard deviation of the binomial distribution.

STEP 3

The mean μ\muμ of a binomial distribution is given by the formula:μ=n×p\mu = n \times pμ=n×pSubstitute n=6 n = 6 n=6 and p=0.5 p = 0.5 p=0.5:μ=6×0.5=3\mu = 6 \times 0.5 = 3μ=6×0.5=3

STEP 4

STEP 5

The standard deviation σ\sigmaσ is the square root of the variance:σ=σ2=1.5≈1.225\sigma = \sqrt{\sigma^2} = \sqrt{1.5} \approx 1.225σ=σ2​=1.5​≈1.225 The mean is:3 \boxed{3} 3​The variance is:1.5 \boxed{1.5} 1.5​The standard deviation is:1.225 \boxed{1.225} 1.225​

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QuestionA fair coin is tossed six times. Find the mean, variance and standard deviations of number of heads obtained. (Round the answers upto 3 decimal places)
Click here to enter an

1. The coin is fair, meaning the probability of heads (success) is $p = 0.5$ .
2. The number of trials (coin tosses) is $n = 6$ .
3. The distribution of the number of heads follows a binomial distribution.

1. Calculate the mean of the binomial distribution.
2. Calculate the variance of the binomial distribution.
3. Calculate the standard deviation of the binomial distribution.

The mean $\mu$ of a binomial distribution is given by the formula:
$\mu = n \times p$
Substitute $n = 6$ and $p = 0.5$ :
$\mu = 6 \times 0.5 = 3$

The standard deviation $\sigma$ is the square root of the variance:
$\sigma = \sqrt{\sigma^2} = \sqrt{1.5} \approx 1.225$
The mean is:
$\boxed{3}$
The variance is:
$\boxed{1.5}$
The standard deviation is:
$\boxed{1.225}$