# 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.

**Q2: **

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

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**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 be the random variable which counts the number of successes. Find the variance of .

**Q5: **

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

**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 be the number of face cards selected in 25 trials. Calculate .

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

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