Multiple Choice
A factory produces lightbulbs in batches of 50. The probability distribution for the number of defective lightbulbs in a randomly selected batch is shown below. Find the expected value.
5. Binomial Distribution & Discrete Random Variables
Discrete Random Variables
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A company tracks the number of complaints they receive, where the random variable X is the number of complaints received daily. Find the variance & standard deviation of this distribution.
A
Variance = 0.83; Standard Deviation = 0.9
B
Variance = 0.9; Standard Deviation = 0.83
C
Variance = 0.83; Standard Deviation = 0.85
D
Variance = 0.85; Standard Deviation = 0.9
Verified step by step guidance1
Calculate the expected value (mean) of the random variable X using the formula: E(X) = Σ [x * P(x)], where x is the number of complaints and P(x) is the probability of x complaints.
Compute the variance using the formula: Var(X) = Σ [(x - E(X))^2 * P(x)], where E(X) is the expected value calculated in the previous step.
To find the standard deviation, take the square root of the variance: SD(X) = √Var(X).
Review the calculated variance and standard deviation values and compare them with the given options to identify the correct answer.
Ensure all calculations are accurate and verify the consistency of the probability distribution (sum of probabilities should equal 1).
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