Questions: A binomial experiment has the given number of trials n and the given success probability p. n=9, p=0.2 Part 1 of 3 (a) Determine the probability P(5). Round the answer to at least four decimal places. P(5)=0.0165 Part: 1 / 3 Part 2 of 3 (b) Find the mean. Round the answer to two decimal places. The mean is

Solution Steps

To solve these problems, we need to use the properties of a binomial distribution.

(a) For the probability \( P(5) \), we use the binomial probability formula: \[ P(k) = \binom{n}{k} p^k (1-p)^{n-k} \] where \( n \) is the number of trials, \( k \) is the number of successes, and \( p \) is the probability of success.

(b) The mean of a binomial distribution is given by: \[ \text{Mean} = n \times p \]

To find the probability of getting exactly 5 successes in 9 trials with a success probability of 0.2, we use the binomial probability formula:

\[ P(5) = \binom{9}{5} (0.2)^5 (0.8)^{4} \]

Calculating this gives:

\[ P(5) \approx 0.0165 \]

The mean of a binomial distribution is calculated using the formula:

\[ \text{Mean} = n \times p \]

Substituting the values:

\[ \text{Mean} = 9 \times 0.2 = 1.8 \]

Final Answer