Binomial and Normal Distributions Review

Front

What are the assumptions of the Binomial distribution?

Back

1. All trials must be independent. 2. Each trial has only two outcomes: success or failure. 3. The number of trials is fixed. 4. The probability of success is constant across trials.

Front

What is the probability of a number being AT LEAST -2.15 on a standard normal curve?

Back

0.9842

Front

What percentage of data falls within one standard deviation of the mean in a normal distribution?

Back

68%.

Front

If the mean of a normally distributed variable is 16 oz and the standard deviation is 0.4 oz, how much soda is in the lightest 22% of cans?

Back

Approximately 15.69 oz.

Front

What is the cut-off temperature for rejecting 12% of thermometers with readings too high, given a mean of 0 degrees Celsius and a standard deviation of 1 degree Celsius?

Back

1.17 degrees Celsius.

Front

Define a Binomial distribution.

Back

A Binomial distribution is a discrete probability distribution that describes the number of successes in a fixed number of independent Bernoulli trials, each with the same probability of success.

Front

What is the formula for calculating the probability of getting exactly k successes in n trials in a Binomial distribution?

Back

Front

What does the Central Limit Theorem state?

Back

The Central Limit Theorem states that the distribution of the sample means approaches a normal distribution as the sample size increases, regardless of the shape of the population distribution.

Front

What is the significance of the standard deviation in a normal distribution?

Back

The standard deviation measures the dispersion or spread of the data points around the mean. In a normal distribution, about 68% of the data falls within one standard deviation of the mean.

Front

What is the z-score and how is it calculated?

Back