1) U.S. Bureau of the Census data reveal the town of Smallville, OH has a population of 10 families. These families own the following: Family X1 X2 X3 X4 X5 X6 X7 X8 X9 X10 Autos XXXXXXXXXX TVs...

Ten families live in Smallville, KS. A sample of five families are surveyed as to the number of
children in the family. The sample data (number of children in the family) is as follows: 2, 7, 3,
2, 6.
Calculate the sample mean number of children.
Sample mean = (2 + 7 + 3 + 2 + 6)/5 = 20/5 = 4
Calculate the sample standard deviation number of children.
Sample Standard deviation = √([(2 – 4)
2
+ (7 – 4)
2
+(3 – 4)
2
+(2 – 4)
2
+(6 – 4)
2
]/(5-1)) = 2.345
The ten families living in Smallville, KS own forty TVs, of which twenty-eight TVs were made
in America. If the local TV repair shop randomly selects five different TVs for inclusion in a
production study, what is the probability of the following:
Given
Probability of owning TV made in America = p = 28/40 = 0.7
Sample size = n = 5
Here, X representing the number of TVs made in America follows binomial distribution
None of the TVs was made in America?
P (X = 0) = 5C0 (0.7)
0
(0.3)
5-0
= 0.00243
At least one of the TVs was made in America?
P (X ≥ 1) = 1 – P (X = 0) = 1 – 0.00243 = 0.99757
The State of KS averages four serial crimes per 100 crimes. If 50 crimes are randomly selected,
what is the probability of the following:
Exactly one crime will be a serial crime? P (X = 1) = 50C1 (0.04)
1
(0.96)
50-1
= 0.271
At most three crimes will be serial crimes? P (X ≤ 3) = 0.13 + 0.271 + 0.276 + 0.184 = 0.861
Over nine crimes will be serial crimes? P (X > 9) = 1 – P (X ≤ 9) = 1 – 0.99998 = 0.00002
In the State of KS, 40 percent of all e-mails deal in some way with the depressed U.S. economy.
If a random sample of 10 e-mails are selected, what is the probability of the following:
Exactly 6 e-mails deal in some way with the depressed U.S. economy?
P (X = 6) = 10C6 (0. 4)
6
(0.6)
10-6
= 0.1115
Exactly 6 e-mails do not deal in some way with the depressed U.S. economy?
P (X =4) = 10C4 (0. 4)
4
(0.6)
10-4
= 0.2508
More than 6 e-mails deal in some way with the depressed U.S. economy?
P (X > 6) = 1 – P (X ≤ 6) = 1 – 0.9452 = 0.0548
U.S. Bureau of the Census data reveal the...