Statistics Chapter 7 Normal Probability Distribution

Intro To Normal Distribution & Standard Normal Distribution

100

What Is The Area In The Bell Shape Curve ?

What is 1 .

200

Where Is u Found In The Curve ?

What is In The Center Or Middle Of The Curve

300

Which statement is true:

1. The curve is allowed to cross the horizontal axis

2. The curve is bell shaped and symmetrical

2

400

What percentage of data falls between 3 standard deviations each way?

99.7

500

What percentage of data falls between 2 standard deviations to the left and 1 to the right?

47.5

Normal Distributions:Finding Probabilities

100

What is the equation for finding the z-score of a normal x distribution?

z = (x - mu) / sigma

200

Suppose mu=32 and sigma=3.2. Find the probability of data that lies TO THE LEFT of x=37

.9406

300

Suppose that mu=41 and sigma=3.4. Find the probability that x will lie TO THE RIGHT of 43.

0.2810

400

What Do You Have To Do First To Find The Area Under Any Normal Curve?

First Convert values to Z-Scores

500

Suppose mu=12 and sigma=1.2. Find the probability of the area between 10.5 and 14.

.8469

Normal Distributions :Finding x and z values

100

What formula is used to convert a z-Score to an x value?

x= zo + u

200

Find z such that 8% of the standard normal curve lies TO THE RIGHT of z.

1.41

300

Find z such that 56% of the data lies between -z and z.

-2.01 and 2.01

400

Find z such that 7.5% of the data lies TO THE LEFT of z.

-1.44

500

Accrotime doesn't want to make refunds for more than 11% of their watches. How long (to the nearest month) should they guarantee the period to be? 

Let o = 5 months and mu = 28months.

21.85 months = 22months

Sampling Distributions & The Central Limit Theorem

100

What are the new formulas when we are looking for a mean (Ex. we pick 5 trout instead of 1)

mu = mu

o = o/sqrt(n)

z = x bar - mu / new sigma

200

According to the central limit theorem, n must be greater than what number? **If the original was not stated as normal?

30

300

What is the equation to find the standard error of a sampling distribution?

o/sqrt(n)

400

Let mu=10.2 and sigma=1.4. What is the MEAN length of 6 trout taken at random is greater than 8.5 inches?

.9986

500

Let mu = 12.1 and sigma = 3.8 minutes. What is the probability that the MEAN time for 50 vehicles in the tunnel will be less than 13 minutes?

0.9525

Normal Approximations To Binomial Distributions

100

What do the following variables represent?

r, n, p, q?

r = number of success

n = number of trials

p = success

q = failure

200

What check do you have to make to determine if the binomial distribution will work?

np > 5 and nq > 5

300

What are the equations for mu and standard deviation?

mu = np

sigma = sqrt(npq)

400

Let n=25, p=0.30 and r >= 9. Find the z score and then probability that matches up with this info.

.6664

500

Let n=500, p=0.65 and we want to test r <= 355. Find the z score and then the corresponding probability.

.9974