Worksheet: The Mean and Standard Deviation of a Binomial Distribution

In this worksheet, we will practice calculating the mean and standard deviation of a binomial random variable.

Q1:

In a binomial experiment, the probability of a success in each trial is 0.6. If 25 trials are performed, what is the median?

Q2:

A binomial experiment has been set up to measure the number of successes, 𝑋, of 𝑛 trials, where the probability of success in each trial is 𝑝. State the expected number of successes.

  • A𝑛𝑝
  • B𝑛𝑝
  • C𝑛𝑝
  • D𝑛𝑝(1𝑝)
  • E𝑛(1𝑝)

Q3:

In a binomial experiment, the probability of a success in each trial is 0.3 and 20 trials are performed. What is the expected number of successful trials?

Q4:

In a binomial experiment, the probability of success in each trial is 0.2 and 40 trials are performed. Let 𝑋 be the random variable which counts the number of successes. Find the variance of 𝑋.

Q5:

In a binomial experiment, the probability of a success in each trial is 0.45 and 30 trials are performed. Let 𝑋 be the random variable which counts the number of successes. Find, to 2 decimal places, the standard deviation of 𝑋.

Q6:

Olivia set up the following binomial experiment to investigate the probability of drawing a face card (jack, queen, or king) from a pack of 52 cards. She performed 25 trials and each trial consisted of randomly selecting 1 of 52 cards. A success is counted as picking a face card.

Let 𝑋 be the number of face cards selected in 25 trials. Calculate 𝑃(𝑋=6).

Find the expected number of face cards selected in 25 trials.

Using her results, calculate the experimental probability of selecting a face card.

Q7:

Suppose the number of children in a family follows a Poisson distribution with mean 𝜇=2.2. Find the probability of finding 1 or more children in the family.

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