Ch. 6 & 7 Test

ReviewDiscrete Probability Distributions

Normal Probability Distributions

6.1: Discrete Probability Distributions

2 Rules for distributions

Sum to 1

Between 0 and 1

Mean, Standard Deviation, Variance of Distributions

Histogram

Interpret Mean

Problems to consider: # 7-10, 11-16, 19, 21, 29-32

Example (#23) The following data represent the

number of games played in each

World Series from 1923 to 2007.

Find and interpret the mean

Find the standard deviation

Find the variance

Crete a histogram

X (games

played)

P(x)

4 .2024

5 .1905

6 .2123

7 .3929

6.2: Binomial Probability Distributions

Criteria for binomial distribution

Find mean, standard deviation, and variance of

binomial distributions

Calculate probabilities of the binomial distribution

Problems to consider: # 17 – 28, # 29-34 (part C

only), 35, 39

Example (#41) A CNN/USA Today/Gallup poll in April 2005 reported that

75% of adult Americans were satisfied with the job the nation’s major airlines were doing. Ten adult Americans are selected at random, and the number who are satisfied are recorded

Find the probability that exactly 6 are satisfied

Find the probability that fewer than 7 are satisfied

Find the probability that 5 or more are satisfied

Find the probability that between 5 and 8, inclusive, are satisfied

Would it be unusual to find 3 or fewer satisfied? Explain.

7.1: Normal Probability Distributions

How the mean and standard deviation effects the

shape of the distribution

The two interpretations for the area under the curve of

a normal distribution

Draw and shade areas of a normal distribution

Problems to consider: # 23, 24, 25-28, 31, 33

Example (#32) The heights of 10-year-old males are normally

distributed with a mean of 55.9 inches and a standard

deviation of 5.7 inches.

Draw a normal curve with the parameters labeled

Shade the region that represents the proportion of 10-

year-old males who are less than 46.5 inches tall.

Suppose that the area under the normal curve to the left

of x = 46.5 is 0.0496. Provide two interpretations of

this result

Probability of randomly choosing a 10-year-old male less

than 46.5 inches tall is 4.96%

4.96% of ten year old males are less than 46.5 inches tall

7.2: Standard Normal Probabilities

Draw, shade, and calculate probabilities of the

standard normal distribution

Find a z-score for a given area (using invnorm)

Problems to consider: # 5-14, 15, 17, 19, 21,

33-44

Examples P(Z < - 0.61) =normalcdf(-9999999,-0.61,0,1)=.2709

P(Z > 1.84) = normalcdf(1.84, 9999999,0,1) = .0329

P(1.23 < Z < 1.56) = normalcdf(1.23, 1.56, 0, 1) = .04997

P(Z < -0.38 or Z > 1.93) = normalcdf(-99999. -.38,0,1) + normalcdf(1.93, 999999, 0,1) = .3788

Z-score for area to left is .8693 = invnorm(.8696,0,1) = 1.123

Z-score for area to the right is .4466 = invnorm(.5534, 0,1) = .1343

7.3: Applications of the Normal

Distribution

Calculate normal probabilities for distributions

outside of standard normal

MUST CONVERT TO STANDARD

NORMAL FIRST

Find the value of a normal random variable

given the area

Problems to consider: # 3 – 12, 17, 19, 21, 25

Example The number of chocolate chips in and 18-ounce bag of Chips

Ahoy! Chocolate chip cookies is approximately normally

distributed with a mean of 1,262 chips and a standard

deviation of 118 chips.

Find the probability that a randomly selected bag of cookies has

less than 1000 chocolate chips.

Find the probability that a randomly selected bag of cookies has

more than 1,350 chocolate chips

Find the probability that a randomly selected bag of cookies has

between 1200 and 1300 chocolate chips.

Suppose a bag of cookies was known to fall at the 90th

percentile, determine the number of chips this bag would

contain.