1. WARM UP
1. A national investigation reveals that 24% of year olds get traffic tickets. You collect a random sample of year olds. What is the Probability that between 45 and 55 of the 200 have received tickets? Check the Assumptions. Change both 45 and 55 to % and find their two z scores.
2. A national investigation reveals that year olds travel an average of 12 miles over the speed limit,
σ = You collect a random sample of year olds. What is the Probability they travel between 15 to 20 miles over the speed limit?
Check the Assumptions

2. 1. A national investigation reveals that 24% of. 16-21 year olds get
1. A national investigation reveals that 24% of year olds get traffic tickets. You collect a random sample of year olds. What is the Probability that between 22.5% & 27.5% of year olds received tickets? Check the Assumptions.
2. A national investigation reveals that year olds travel an average of 12 miles over the speed limit, σ = You collect a random sample of year olds. What is the Probability they travel between 15 to 20 miles over the speed limit?
Proceed with Caution! PWC

3. THE CENTRAL LIMIT THEOREM (C.L.T.): Shape
The Central Limit Theorem states that the sampling distribution of mean or proportion will be Approximately Normal, regardless of the distribution of the population, as long as the n is Large, & the observations are independent and collected by an SRS.
THE LAW OF LARGE NUMBERS: Center
As the number of observations, n, increases, the closer and closer the mean gets to the true population mean.

4. Sampling Distribution of Pennies2 4 9 14 21 27 66
142 13
1958
1963
1968
1973
1978
1983
1988
1993
1998
2003
2008
150 –
125 –
100 –
75 –
50 –
25 –
0 –
Penny’s Date
n = 35
n = 25

5. EXAMPLE: In a large factory batch of M&M’s it is stated that 12% of the candies will be green. You collect a random sample of 86 M&M’s. What is the probability that less than 10% of the candies will be green?

6. EXAMPLE: The weight of a bag of Potato Chips is supposed to have mean = 20.4 oz with std. dev.= 1.24 oz. The product is declared underweight if it weighs less than 18 oz which is stated on the bag.
With a SRS sample of 34 bags find the probability that the Product will be underweight.
Collected by an SRS, and Approximately Normal: n>30 -> C.L.T.

7. HW Page 430: 25(c,d), 36(c,d),37, 38

8. HW Page 430: 25(c,d), 36(c,d),37, 38

10. EXAMPLE: The weight of a bag of Potato Chips is supposed to have mean = 20.4 oz with std. dev.= 1.24 oz. The product is declared underweight if it weighs less than 18 oz which is stated on the bag.
With a SRS sample of a single bag find the probability that the product is underweight. Assume a Normal Population.
With a SRS sample of 34 bags find the probability that the Product will be underweight.
Approximately Normal –Stated And Collected by an SRS.
Approximately Normal: n>30 -> C.L.T. And Collected by an SRS.

11. Finding Sample Mean Observations, (x) from Probabilities
EXAMPLE: Assume that the rainfall in Ithaca, NY is Appr. Normal with mean: inches and Std Dev.: 4.2”. Less than how much rain falls in the driest 20% of all years
z = invNorm(.20)=
20%
x=?
x = ”

12. Finding Sample Mean Observations, (x) from Probabilities
EXAMPLE: Assume that the duration of human pregnancies is Appr. Normal with mean: 266 days and Std Dev.: At least how many days should the longest 25% of all pregnancies last?
z = invNorm(.75)= .6745
25%
x=?
x =

13. 1. The Test over Chapter ninteen has traditionally. had a mean of 86
1. The Test over Chapter ninteen has traditionally had a mean of 86.2% with a std. deviation of %. Assume the data follows a Normal distribution.
a.) If a student is selected at random, what is the probability that he or she will score above 90%?
b.) If 16 students are selected at random, what is the probability that their average will be above 90%?
c.) Draw the Sampling Distribution Normal Curves for both a and b. On both graphs label all six standard deviations
(± 3s) for the

14. With μ = 86.2% and σ = 8.5%. a.) When n = 1 the b.) When n = 16 the
c.).
86.2
88.3
92.6
90.5
79.8
82.0
84.1