Multiple Choice
Which of the following cannot be modeled by a continuous distribution?
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5. Binomial Distribution & Discrete Random Variables
Discrete Random Variables
Multiple Choice
Which of the following is an example of a binomial random variable?
A
The number of heads obtained when flipping a fair coin times
B
The time it takes for a student to finish an exam
C
The weight of apples in a basket
D
The number of cars passing through an intersection in hour
Verified step by step guidance1
Step 1: Understand the definition of a binomial random variable. A binomial random variable counts the number of successes in a fixed number of independent trials, where each trial has only two possible outcomes (success or failure) and the probability of success is constant across trials.
Step 2: Analyze each option to see if it fits the binomial criteria: fixed number of trials, two possible outcomes per trial, independence, and constant probability.
Step 3: For 'The number of heads obtained when flipping a fair coin 10 times': There are 10 fixed trials (coin flips), each with two outcomes (head or tail), independent flips, and a constant probability of heads (0.5). This matches the binomial setup.
Step 4: For 'The time it takes for a student to finish an exam': This is a continuous measurement, not counting successes in trials, so it is not binomial.
Step 5: For 'The weight of apples in a basket' and 'The number of cars passing through an intersection in one hour': Both are not counting successes in fixed trials with two outcomes; weight is continuous, and cars passing is a count but not from fixed trials with two outcomes, so neither is binomial.
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