Solved on Mar 07, 2024

Find the formula for the binomial probability mass function $p(x)$ with $n=7$ and $p=0.8$ . $p(x) = \binom{7}{x}(0.8)^x(0.2)^{7-x}$ for $x=0,1,2,\ldots,7$ .

STEP 1

Assumptions
1. The number of trials $n$ is 7.
2. The probability of success $p$ is 0.8.
3. The probability of failure $q$ is $1 - p$ .
4. The value of $x$ represents the number of successes, which can range from 0 to $n$ .
5. The binomial probability formula is given by: $p(x) = \binom{n}{x}p^xq^{n-x}$ where $\binom{n}{x}$ is the binomial coefficient representing the number of ways to choose $x$ successes from $n$ trials.

STEP 2

First, we need to find the probability of failure $q$ .
$q = 1 - p$

STEP 3

Now, plug in the given value for $p$ to calculate $q$ .
$q = 1 - 0.8$

STEP 4

Calculate the probability of failure $q$ .
$q = 1 - 0.8 = 0.2$

STEP 5

With $n=7$ , $p=0.8$ , and $q=0.2$ , we can now write the formula for $p(x)$ for a binomial random variable.
$p(x) = \binom{7}{x}(0.8)^x(0.2)^{7-x}$

STEP 6

We also need to specify the range of $x$ in the formula.
$x = 0, 1, 2, \ldots, 7$

STEP 7

Finally, we can write the complete formula for $p(x)$ as:
$p(x) = \binom{7}{x}(0.8)^x(0.2)^{7-x} \quad (x = 0, 1, 2, \ldots, 7)$
This is the formula for $p(x)$ for a binomial random variable with $n=7$ and $p=0.8$ .

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Find the formula for the binomial probability mass function $p(x)$ with $n=7$ and $p=0.8$ . $p(x) = \binom{7}{x}(0.8)^x(0.2)^{7-x}$ for $x=0,1,2,\ldots,7$ .

STEP 1

STEP 2

First, we need to find the probability of failure $q$ .
$q = 1 - p$

STEP 3

Now, plug in the given value for $p$ to calculate $q$ .
$q = 1 - 0.8$

STEP 4

Calculate the probability of failure $q$ .
$q = 1 - 0.8 = 0.2$

STEP 5

With $n=7$ , $p=0.8$ , and $q=0.2$ , we can now write the formula for $p(x)$ for a binomial random variable.
$p(x) = \binom{7}{x}(0.8)^x(0.2)^{7-x}$

STEP 6

We also need to specify the range of $x$ in the formula.
$x = 0, 1, 2, \ldots, 7$

STEP 7

Finally, we can write the complete formula for $p(x)$ as:
$p(x) = \binom{7}{x}(0.8)^x(0.2)^{7-x} \quad (x = 0, 1, 2, \ldots, 7)$
This is the formula for $p(x)$ for a binomial random variable with $n=7$ and $p=0.8$ .

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Find the formula for the binomial probability mass function p(x)p(x)p(x) with n=7n=7n=7 and p=0.8p=0.8p=0.8. p(x)=(7x)(0.8)x(0.2)7−xp(x) = \binom{7}{x}(0.8)^x(0.2)^{7-x}p(x)=(x7​)(0.8)x(0.2)7−x for x=0,1,2,…,7x=0,1,2,\ldots,7x=0,1,2,…,7.

STEP 1

STEP 2

First, we need to find the probability of failure qqq.q=1−pq = 1 - pq=1−p

STEP 3

Now, plug in the given value for ppp to calculate qqq.q=1−0.8q = 1 - 0.8q=1−0.8

STEP 4

Calculate the probability of failure qqq.q=1−0.8=0.2q = 1 - 0.8 = 0.2q=1−0.8=0.2

STEP 5

With n=7n=7n=7, p=0.8p=0.8p=0.8, and q=0.2q=0.2q=0.2, we can now write the formula for p(x)p(x)p(x) for a binomial random variable.p(x)=(7x)(0.8)x(0.2)7−x p(x) = \binom{7}{x}(0.8)^x(0.2)^{7-x} p(x)=(x7​)(0.8)x(0.2)7−x

STEP 6

We also need to specify the range of xxx in the formula.x=0,1,2,…,7 x = 0, 1, 2, \ldots, 7 x=0,1,2,…,7

STEP 7

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Find the formula for the binomial probability mass function $p(x)$ with $n=7$ and $p=0.8$ . $p(x) = \binom{7}{x}(0.8)^x(0.2)^{7-x}$ for $x=0,1,2,\ldots,7$ .

First, we need to find the probability of failure $q$ .
$q = 1 - p$

Now, plug in the given value for $p$ to calculate $q$ .
$q = 1 - 0.8$

Calculate the probability of failure $q$ .
$q = 1 - 0.8 = 0.2$

With $n=7$ , $p=0.8$ , and $q=0.2$ , we can now write the formula for $p(x)$ for a binomial random variable.
$p(x) = \binom{7}{x}(0.8)^x(0.2)^{7-x}$

We also need to specify the range of $x$ in the formula.
$x = 0, 1, 2, \ldots, 7$