biostats2010 week 4a part 2

Normal Distribution

A probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean.

Left Tail Probability

The probability that a random variable is less than a certain value, represented by the area under the curve to the left of that value.

Right Tail Probability

The probability that a random variable is greater than a certain value, represented by the area under the curve to the right of that value.

Cumulative Probability

The probability that a random variable takes on a value less than or equal to a certain value.

Z Score

A statistical measurement that describes a value's relation to the mean of a group of values, calculated as (X - mean) / standard deviation.

Z Critical Value

The value of Z that corresponds to a specified probability in the standard normal distribution.

Inverse Norm Function

A calculator function used to find the value corresponding to a given cumulative probability in a normal distribution.

Mean (μ)

The average of a set of values, a measure of central tendency.

Standard Deviation (σ)

A measure of the amount of variation or dispersion in a set of values.

Probability Density Function

A function that describes the likelihood of a random variable to take on a particular value.

QQ Plot

A graphical tool to assess if a dataset follows a normal distribution by plotting observed values against expected normal Z scores.

Binomial Distribution

A probability distribution that summarizes the likelihood that a value will take on one of two independent outcomes, often referred to as "success" or "failure."

Normal Approximation

The use of the normal distribution to approximate the binomial distribution when the number of trials is large and the probability of success is not too close to 0 or 1.

Sample Size (n)

The number of observations in a sample, which affects the accuracy of statistical estimates.

Probability of Success (p)

The likelihood of a successful outcome in a single trial of a binomial experiment.

What is the main focus of the biostats week 4a part 2 lecture?

The normal distribution and its applications.

What types of probabilities can be calculated in the normal distribution?

Left tail, right tail, and probabilities between two values.

What does the table provide in terms of probabilities?

Left tail probabilities only.

How do you find a right tail probability using the table?

Use symmetry or the complement of the left tail probability.

What is the formula to convert a z-score back to a data point?

x = z * σ + μ.

What is the mean and standard deviation for the sleep example discussed?

Mean = 6.8 hours, Standard deviation = 0.6 hours.

What is the probability of a person sleeping between 7 and 8 hours?

Approximately 0.34.

What is the first step when calculating probabilities with a calculator?

Identify the type of probability (left tail, right tail, or between two values).

What is the inverse norm function used for?

To find a value corresponding to a given left or right tail probability.

What is the mean and standard deviation for the weight gain example in diabetic patients?

Mean = 12, Standard deviation = 12.

How do you assess if a variable is normally distributed?

By examining histograms and QQ plots.

What are the two parameters in the binomial distribution?

n (total number of trials) and p (probability of success).

When can the normal distribution be used to approximate the binomial distribution?

When n is large and np and n(1-p) are both greater than 10.

What is the expected value in a binomial distribution?

n * p.

What is the probability that 1,524 or more adults are overweight or obese in a sample of 2,500?

Approximately 0.201.