Part 3 of 4 (c) What is the probability that fewer than 4 weigh more than 20 pounds? The probability that fewer than 4 weigh more than 20 pounds is $$ \square $$.

Question

UpStudy AI · Accepted Answer

To solve the problem of finding the probability that fewer than 4 out of a certain number of items weigh more than 20 pounds, we need to know the following:

1. The total number of items (let's denote this as $$ n $$).
2. The probability that a single item weighs more than 20 pounds (let's denote this as $$ p $$).
3. The distribution of the number of items that weigh more than 20 pounds.

Assuming that the number of items that weigh more than 20 pounds follows a binomial distribution, we can denote the number of items that weigh more than 20 pounds as $$ X $$, where $$ X \sim \text{Binomial}(n, p) $$.

The probability that fewer than 4 items weigh more than 20 pounds can be expressed as:

$$
P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)
$$

The probability mass function for a binomial distribution is given by:

$$
P(X = k) = \binom{n}{k} p^k (1-p)^{n-k}
$$

where $$ \binom{n}{k} $$ is the binomial coefficient.

To proceed, please provide the values for $$ n $$ (the total number of items) and $$ p $$ (the probability that a single item weighs more than 20 pounds).
To find the probability that fewer than 4 items weigh more than 20 pounds, we need to know the total number of items ($$ n $$) and the probability that a single item weighs more than 20 pounds ($$ p $$). Using the binomial distribution formula: $$ P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) $$ Each term $$ P(X = k) $$ is calculated as: $$ P(X = k) = \binom{n}{k} p^k (1-p)^{n-k} $$ Please provide the values of $$ n $$ and $$ p $$ to compute the exact probability.

Part 3 of 4 (c) What is the probability that fewer than 4 weigh more than 20 pounds? The probability that fewer than 4 weigh more than 20 pounds is \( \square \).

Upstudy AI Solution

Answer

Solution

Beyond the Answer

Related Questions

Latest Probability Questions