829254 0232195 431 1421651 155 1586604 0411993 50

9.829254 0.232195 0.047367 3.0
8.375431 1.421651 2.999985 4.0
3.135155 15.86604 0.411993 5.0
12.11597 4.174701 1.464274 7.0
1.697451 3.635592 9.590034 5.0
8.551382 12.85992 23.5624 12.0
1.232774 13.00607 0.712347 6.0
3.941296 10.55612 1.931498 4.0
3.412402 0.977313 3.590985 6.0
8.129921 1.830953 3.365595 3.0
9.020216 1.705849 0.783159 4.0
4.604425 0.660299 9.940817 5.0
3.752413 21.34168 1.344384 6.0

0.928675 18.4968 5.343458 7.0
4.343439 0.115791 6.193506 5.0
8.105304 6.238134 7.728982 5.0
4.688775 0.057882 2.562954 2.0
5.228386 0.102552 1.500589 3.0
6.076004 3.087259 2.848419 5.0
3.038776 2.338413 2.191178 4.0
4.672079 2.696659 0.526879 3.0
3.542982 10.74425 2.322607 5.0
5.663312 6.949428 0.863821 5.0
7.369389 10.64668 3.974903 6.0
6.855821 13.19186 1.183727 8.0
0.513084 11.84029 0.981783 4.0
2.847589 4.456933 2.061544 3.0
6.288525 0.846614 1.957629 6.0
4.330803 7.666323 1.809161 6.0
6.234556 1.831595 4.218052 4.0
4.745876 2.53803 3.636736 3.0
1.967847 2.509912 1.84134 6.0
0.731377 5.461138 3.655829 4.0
0.713383 1.477312 1.727201 3.0
3.714311 7.5798 3.647227 4.0
4.018314 3.264818 3.619365 5.0
11.387 4.484027 0.626805 8.0
0.144315 2.851204 7.966311 5.0
1.340965 2.155356 12.12027 4.0
5.513043 3.140254 3.349841 3.0
4.474311 0.891851 15.61361 5.0
7.112833 1.167993 9.326367 4.0
0.34196 3.735136 0.694424 2.0
14.291 8.91795 1.918667 7.0
0.388773 4.684261 0.023321 6.0
11.41131 5.162464 1.419194 6.0
0.170053 13.33469 5.926041 4.0
16.76247 0.698274 1.744201 4.0
3.155117 5.905853 0.582206 4.0
19.53596 2.460933 0.922153 7.0
0.019918 6.860389 3.975215 3.0
1.948222 3.942688 4.425905 2.0
4.287233 0.130439 2.941371 3.0
2.791392 10.13996 11.25588 8.0
0.445896 19.11389 12.97505 8.0
6.828451 9.480077 1.604902 7.0
4.886092 4.104976 12.24935 6.0
12.37646 2.322459 2.196102 5.0

1.384909 1.71143 9.702321 4.0
2.407626 4.256256 12.51078 6.0
2.346045 9.136626 1.381957 5.0
3.815828 3.06555 1.801899 4.0
5.265143 6.465851 11.42774 6.0
3.918272 10.43979 3.672597 4.0
0.821362 1.469272 0.550012 3.0
6.765838 12.33199 3.007814 9.0
11.07313 7.155214 0.380462 5.0
8.584115 3.094883 0.091394 6.0
8.158518 7.316212 4.443862 5.0
1.859072 0.629452 13.69583 4.0
7.882248 3.150256 0.316092 4.0
6.511967 5.686449 12.86564 10.0
1.665934 0.236138 25.76461 7.0
0.993037 1.080471 1.532599 2.0
3.067547 0.223201 2.511721 2.0
1.701092 3.493319 2.28267 2.0
18.02797 6.145919 0.570076 9.0
0.605899 7.057879 3.485346 3.0
32.40417 0.139953 1.932378 11.0
1.28298 2.433205 3.73639 3.0
0.657778 3.427911 4.146364 3.0
5.623043 0.792864 10.26594 4.0
0.945939 0.692133 1.992568 2.0
0.080142 0.069759 2.065565 1.0
0.947819 29.18638 14.94949 11.0
1.876692 1.572598 0.967503 3.0
9.198971 1.37903 1.442134 5.0
6.802473 6.666664 10.81489 7.0
2.960495 6.116368 3.244342 6.0
2.685102 11.4653 2.07237 5.0
2.352584 14.40041 1.018909 4.0
3.769125 9.321104 2.240641 4.0
18.67721 2.862975 5.102389 6.0
2.977543 15.29933 9.161957 7.0
7.922134 1.2035 39.67296 12.0
0.432816 3.94607 13.53894 5.0
3.282947 2.919402 5.011016 5.0
0.315245 0.456505 3.119753 3.0
1.613631 13.7236 6.257144 6.0
0.20196 1.438458 7.039756 3.0
1.671457 3.716255 2.377151 3.0
0.335972 7.658635 3.372519 4.0
1.017558 1.148256 4.719436 2.0

2.19076 0.983625 4.85507 3.0
5.30451 5.6606 0.110587 3.0
4.338613 1.909353 7.536002 9.0
8.627822 0.129294 3.256608 6.0
3.863478 0.023359 7.675608 4.0
1.779236 1.716796 10.05159 3.0
3.121299 4.330569 1.253643 2.0
3.606528 15.61994 1.453399 8.0
2.724159 0.888373 11.16816 3.0
9.110579 5.49657 6.432793 5.0
0.417208 3.093254 0.653065 2.0
35.66023 3.359607 7.706747 10.0
7.40172 3.424044 3.8719 4.0
8.810041 7.585266 6.59919 6.0
0.737112 3.776291 0.538561 6.0
0.977195 4.875056 2.992479 12.0
15.87015 0.96118 8.586908 6.0
13.1494 3.220909 1.824743 4.0
2.358013 2.33194 13.01272 6.0
9.422029 9.06483 0.129717 4.0
1.037931 17.34174 6.773735 7.0
0.323877 8.216733 5.337039 6.0
6.585712 1.449312 2.01959 4.0
6.867369 1.695344 2.717458 4.0
11.17576 2.417706 2.110007 7.0
5.800729 0.829963 4.968544 4.0
11.37361 14.59626 1.710176 9.0
2.217401 7.700614 2.786512 3.0
0.821117 2.706216 8.158242 2.0
14.18954 13.36069 1.271473 7.0
7.798106 0.678985 1.300901 3.0
12.17385 1.673364 1.650565 5.0
3.726181 16.84403 3.444734 6.0
3.908141 8.915701 14.26073 8.0

4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Bins

Example 1
μ 12%
σ 3.60%
n 9
0.012 Standard deviation of sample = SD of population/SQRT(n)
X 14.40%
z score 1.833 z score= X-MEAN/SD OF SAMPLE
> X 3.34%
Example 2
μ $70,000.00
σ $5,000.00
n 36
$833.33 Standard deviation of sample = SD of population/SQRT(n)
X $72,300
z score 2.76
> X 0.29% Probability (upper tail) of getting a mean income of $72,300 or hi
Suppose, that based on historical data, we believe that the annual percentage salary increases for the C
corporations are normally distributed with a mean of 12.2% and a standard deviation of 3.6%. A random
observations is obtained from this population, and the sample mean is computed. What is the probabili
mean will be greater than 14.4%.?
σ
s
Antelope coffee is considering a possibility of opening a gourmet coffee shop in Big Rock, Montana. Prev
that its shops will be successful in cities of this size if the mean annual family income is above $70,000. I
standard deviation of income is $5,000 in Big Rock, Montana. A random sample of 36 people was obtain
$72,300. Does this sample provide evidence to conclude that a shop should be opened?
σ
s

igher.
CEOs of all midsize
m sample of nine
ity that the sample
vious research has indicated
It is also assumed that the
ned, and the mean income was

n 270
P 20%
1-P 80%
X1 16%
X2 24%
0.06%
2.43%
Cumulative Probability
Upper 95.0%
Lower 5.0%
Difference 90.0%
A random sample of 270 homes was taken from a large population of older homes to
estimate the proportion of homes with unsafe wiring. If in fact, 20% of homes have
unsafe wiring, what is the probability that the sample proportion will be between 16%
and 24%?
σ
p
2
σ
p

n 80
P 43%
1-P 57%
X2 50%
0.31%
5.54%
Cumulative Probability
Upper 89.7%
Difference 10.3%
It has been estimated that 43% of business graduates believe that a course in
business ethics is very important for imparting ethical values to students. Find the
probability that more than 1/2 of a random sample of 80 business graduates have
this belief.