(c) $$ n=52, p=\frac{4}{5} $$ Mean: $$ \mu=\square imes 6 $$ Variance: $$ \sigma^{2}=\square $$

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(c) $$ n=52, p=\frac{4}{5} $$ Mean: $$ \mu=\square 	imes 6 $$ Variance: $$ \sigma^{2}=\square $$

UpStudy AI · Accepted Answer

To find the mean and variance of a binomial distribution, we can use the formulas:

Mean: $$ \mu = np $$
Variance: $$ \sigma^{2} = np(1-p) $$

Given:
$$ n = 52 $$
$$ p = \frac{4}{5} $$

Let's calculate the mean and variance using the formulas.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{52	imes 4}{5}$$
- step1: Multiply the numbers:
  $$\frac{208}{5}$$
The mean of the binomial distribution is $$ \mu = 41.6 $$.

Now, let's calculate the variance.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{52	imes 4}{5}\left(1-\frac{4}{5}ight)$$
- step1: Subtract the numbers:
  $$\frac{52	imes 4}{5}	imes \frac{1}{5}$$
- step2: Multiply the numbers:
  $$\frac{208}{5}	imes \frac{1}{5}$$
- step3: Multiply the fractions:
  $$\frac{208}{5	imes 5}$$
- step4: Multiply:
  $$\frac{208}{25}$$
The variance of the binomial distribution is $$ \sigma^{2} = 8.32 $$.

Therefore, the mean is $$ \mu = 41.6 $$ and the variance is $$ \sigma^{2} = 8.32 $$.
Mean: $$ \mu = 41.6 $$ Variance: $$ \sigma^{2} = 8.32 $$

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