QuestionJuly 15, 2025

A binomial probability experiment is conducted with the given parameters. Use Excel to find the probability of x successes in the n independent trials of the experiment. n=6,p=0.2,xlt 4 P(Xlt 4)=square (Round to four decimal places as needed.)

A binomial probability experiment is conducted with the given parameters. Use Excel to find the probability of x successes in the n independent trials of the experiment. n=6,p=0.2,xlt 4 P(Xlt 4)=square (Round to four decimal places as needed.)
A binomial probability experiment is conducted with the given parameters. Use Excel to find the probability of x successes in the n independent trials of the experiment. n=6,p=0.2,xlt 4 P(Xlt 4)=square (Round to four decimal places as needed.)

Solution
3.2(288 votes)

Answer

0.9837 Explanation 1. Identify the Binomial Probability Formula The probability of exactly x successes in n trials is given by **P(X = x) = \binom{n}{x} p^x (1-p)^{n-x}**. 2. Calculate Individual Probabilities For x = 0, 1, 2, 3, calculate P(X = x) using Excel: - P(X = 0) = \binom{6}{0} (0.2)^0 (0.8)^6 - P(X = 1) = \binom{6}{1} (0.2)^1 (0.8)^5 - P(X = 2) = \binom{6}{2} (0.2)^2 (0.8)^4 - P(X = 3) = \binom{6}{3} (0.2)^3 (0.8)^3 3. Sum the Probabilities Use Excel to sum these probabilities: P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3).

Explanation

1. Identify the Binomial Probability Formula<br /> The probability of exactly $x$ successes in $n$ trials is given by **$P(X = x) = \binom{n}{x} p^x (1-p)^{n-x}$**.<br /><br />2. Calculate Individual Probabilities<br /> For $x = 0, 1, 2, 3$, calculate $P(X = x)$ using Excel:<br />- $P(X = 0) = \binom{6}{0} (0.2)^0 (0.8)^6$<br />- $P(X = 1) = \binom{6}{1} (0.2)^1 (0.8)^5$<br />- $P(X = 2) = \binom{6}{2} (0.2)^2 (0.8)^4$<br />- $P(X = 3) = \binom{6}{3} (0.2)^3 (0.8)^3$<br /><br />3. Sum the Probabilities<br /> Use Excel to sum these probabilities: $P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)$.
Click to rate:

Similar Questions