statistics exam 2

there are 15 runners in a race. how many ways can the runners finish first, second, and third?

15!/12! = (15 * 14 * 13) = 2,730

Assume the random variable x is normally distributed with mean μ = 84 and standard deviation σ = 4. Find the indicated probability. P(x < 79)

Answer 1. Convert x of 79 into a z score. z = (79 - 84)/4 z = -1.25 2. Find probability using the z-score P(z < -1.25) = 0.1056 P(x < 79) = 0.1056

a new drug has a 70% compliance rate. 50% of those patients in the course make lifestyle changes. find the probability that a patient complies and makes lifestyle changes.

0.7 * 0.5 = .35

What is the total area under the normal curve?

1

For a standard normal curve (mean = 0, standard deviation = 1) find the area between the two z-scores listed: z = 0 and z = 1.05. (*Hint - you will need to use the Standard Normal Table to answer this question.) Area (0 < z < 1.05)

.3531

Find the probability of z occurring within the following range of z-scores in a standard normal distribution. P(0 < z < 1.77)

.4616

Each outcome in a sample space is equally likely

Classical probability

In a normal distribution, which is great, the mean or the median?

Neither, in a normal distribution, the mean and median are always equal.

In a survey of women in a certain country (ages 20 - 29), the mean height was 66.4 inches with a standard deviation of 2.94 inches. (*Hint - you will need to use the Standard Normal Table to answer this question.) a. What height represents the 95th percentile? b. What height represents the 25th percentile?

a. 71.2363 b. 64.4302

a selection of r objects from a group of n objects without regard to order

combination

the probability of an event occurring, given that another event has already occurred

conditional probability

Based on observations obtained from probability experiments

empirical probability

True or false: the sampling distribution is only normal when the population is normal.

false

if the curve is flat and wide what does that mean?

greater standard deviation

the occurrence of one event does not affect the probability of the occurrence of the other event

independent events

For a population with a mean μ = 74 and a standard deviation σ = 12. Find the mean and the standard deviation of a sampling distribution of sample means with sample size of n = 36.

mean = 74 standard error = 2

Fundamental Counting Rule

multiply the number of outcomes by eachother

two events cannot occur at the same time

mutually exclusive

can a graph that is skewed be represented with a normal distribution?

no

what is the difference between an outcome and an event?

outcome = result of single probability experiment event = set of one or more possible outcomes

an ordered arrangement of objects

permutation

standard deviation of sampling distribution of sample means: is also known as what?

sampling error

intuition, educated guess, and estimates

subjective probability

the highest point of the curve is what?

the mean

how you can transform a nonstandard normal distribution to the standard normal distribution and the formula you would need to use to do so.

use the formula for z-scores to set each value in the normally distributed random variable x to a z-score. z = (x-u) / σ

what is the formula for z score?

z = (x - μ)/σ

symbol for mean

μ

symbol for standard deviation

σ

the equation for sampling error

σ / square root of n