biostats2010 week 4a part 2

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30 Terms

1

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.

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2

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.

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3

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.

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4

Cumulative Probability

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

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5

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.

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6

Z Critical Value

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

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7

Inverse Norm Function

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

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8

Mean (ฮผ)

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

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9

Standard Deviation (ฯƒ)

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

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10

Probability Density Function

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

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11

QQ Plot

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

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12

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."

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13

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.

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14

Sample Size (n)

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

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15

Probability of Success (p)

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

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16

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

The normal distribution and its applications.

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17

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

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

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18

What does the table provide in terms of probabilities?

Left tail probabilities only.

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19

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

Use symmetry or the complement of the left tail probability.

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20

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

x = z * ฯƒ + ฮผ.

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21

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

Mean = 6.8 hours, Standard deviation = 0.6 hours.

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22

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

Approximately 0.34.

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23

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

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

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24

What is the inverse norm function used for?

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

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25

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

Mean = 12, Standard deviation = 12.

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26

How do you assess if a variable is normally distributed?

By examining histograms and QQ plots.

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27

What are the two parameters in the binomial distribution?

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

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28

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.

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29

What is the expected value in a binomial distribution?

n * p.

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30

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

Approximately 0.201.

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