Probability & Statistics
HW 7 - Chebyshev & Empirical & Z score
1.
Name_______________
The average IQ of the students in one calculus class is 110, with a standard deviation of 5; the
average IQ of students in another class is 106, with a standard deviation of 4. A student has an IQ
of 112, in which class is he ranked higher?
2. The average price of the wagon at Car Dealer A is $25,000, with a standard deviation of $4000. The
average price at Car Dealer B is $20,000, with a standard deviation of $2000. If I spent $23,000 at
dealer A and my sister paid $18,000 at dealer B, which was a better deal?
3. The average score on an English final examination was 85, with a standard deviation of 5; the average
score on a history final exam was 110, with a standard deviation of 8. I made an 80 on the English
test and a 100 on the history test. Which test was better?
4. The average age of the accountants at Three Rivers Corp. is 26, with a standard deviation of 6; the
average salary of the accountants is $31,000 with a standard deviation of $4000. I'm applying at
both places and I'm 31 and want to make $35,000, in which category will I be higher?
5. Using Chebyshev's theorem, solve the following problems for a distribution with a mean of 80 and a
standard deviation of 10
a.
At least what percentage of values will fall between 60 and 100?
b. At least what percentage of values will fall between 65 and 95?
6. The mean of a distribution is 20 and the standard deviation is 2. Answer each using Chebyshev's
theorem.
a.
At least what percentage of the values will fall between 10 and 30?
b. At least what percentage of the values will fall between 12 and 28?
7. The mean of a distribution is 50 and the standard deviation is 5. Answer each using The Empirical
Rule.
a.
At least what percentage of the values will fall between 45 and 55?
b. At least what percentage of the values will fall between 35 and 65?
8. A sample of the hourly wages of employees who work in restaurants in a large city has a mean of
$8.58 and a standard deviation of $1.29.
a.
Using Chebyshev's theorem, find the range in which at least 75% of the data values will fall.
b. Using the Empirical Rule, find the range in which at least 95% of the data values will fall.
9. A sample of the labor costs per hour to assemble a certain product has a mean of $15.72 and a
standard deviation of $2.15. Using Chebyshev's theorem, find the values in which at least 88.89% of
the data will lie.
10. The average score on a special test of knowledge of wood refinishing has a mean of 53 and a standard
deviation of 6. Using the Empirical Rule, find the values in which at least 68% of the data will lie.