Question

robem(1) Applications of statisties can be divided into two broad descript Andmernal states. Use your own words to briefly define what descriptive statistics is and what inferential statistics is? Problem(2) Someone mention to you that there is a 6 6 9596-99% rule in statistics te your own words (or graph) to (briefly) explain what this rule is about? Problem(3) A sample (data set) contains the observations 13 12 15 10 9 11 16 find (a) the sample size? (b) , (c) 1, (d) L(x,-1) (c) EL,(x,-1) (0) (1,) 8) the sample mean? (h) the sample variance ? () the sample standard deviation? 6) the sample median? (k) Is there a sample , (,-1)ET, Recall that 32 - )" 1 Problem(4) At a medical center, a sample of 20 days showed the following number of cardiograms done each day. (Hint: 0 ; -661, 2017 = 25665.) 25 31 20 32 13 14 13 02 57 23 36 32 33 32 44 32 52 44 51 45 (a) Find the sample mean i. (b) Find the sample variance s. (The formula for s' has been given in previous problem.) (c) Construct a stem-leaf plot for the data. Problem(5) Consider a random experiment of throwing two fair dice together. (a) Describe the sample space S and assign probabilities to each sample point in S. (b) Let X be the random variable that corresponds to the sum of the two dice. What are the values that the random variable X takes? (c) Find P(X = 8). (d) Find P(X < 4. (e) Find P(x 3). Problem(6) Inspector A visually inspected 1000 ceramic mugs and found flaws in 36 of them. Inspector B inspected the same 1000 ceramic mugs and found flaws in 42 of them. A total of 950 mugs were found to be good by both inspectors. One of the 1000 mugs is selected randomly. (a) Find the probability that a flaw was found in this mug by at least one of the two inspectors. (b) Find the probability that flaws were found in this mug by both inspectors. (c) Find the probability that a flaw was found by inspector B but not by inspector A.

Answer 1

3)

X	X²	(Xi-1)²	(X - X̄)²
13	169	144	0.51
12	144	121	0.08
15	225	196	7.37
10	100	81	5.22
9	81	64	10.80
11	121	100	1.65
16	256	225	13.796

a) sample size = 7

b) Σxi = 13+12+15+10+9+11+16 = 86

c) Σx² = 13²+12²+15²+10²+9²+11²+16² = 1096

d) Σ(X-1) = Σx - 7 = 86-7 = 79

e) Σ(Xi - 1)² = 931

f) (Σxi)² = 86² = 7396

g) mean =    ΣX/n =    86.000   /   7   =   12.2857
                      
h) sample variance =    Σ(X - X̄)²/(n-1)=   39.4286   /   6   =   6.571
                      
i) sample std dev =   √ [ Σ(X - X̄)²/(n-1)] =   √   (39.4286/6)   =       2.563

j) sample median = 4th   value of sorted data = 12  

k) sample mode=there is no mode