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Seminar 08.
Normal Distribution
Practice in Using Normal Tables. Let Z be a standard normal variable
1. Find the area to the left of a given point: 1; 1.12; -1.87; 2; -2; 5; -5.
Find the area to the right of a given point: 1; 1.12; 2,
2. Find z-score for the given probability 0.8982 to the left of it; find the z-score with an area of 0.72 to the
right of it,
3. Find
Pr( Z  1) , Pr( Z  1) , Pr(| Z | 1) , Pr(2 Z  1  3) , Pr(| Z  1| 1.5) ,
4. Find number c such that Pr( Z  c)  0.95 ,
Pr(| Z | c)  0.95
Pr( Z 2  2) .
Pr(| Z | c)  0.99
Free Response problems (using z-scores)
5. The life expectancy of a particular brand of light bulb is normally distributed with a mean of 1500 hours and
a standard deviation of 75 hours.
a. What is the probability that a light bulb will last less than 1410 hours?
b. What is the probability that a light bulb will last between 1563 and 1648 hours?
6. A packing machine is set to fill a cardboard box with a mean average of 16.1 ounces of cereal. Suppose the
amounts per box form a normal distribution with a standard deviation equal to 0.04 ounce.
a. What percentage of the boxes will end up with at least 1 pound of cereal?
b. Ten percent of the boxes will contain less than what number of ounces?
c. Eighty percent of the boxes will contain more than what number of ounces?
d. The middle 90% of the boxes will be between what two weights?
7. Suppose that the average height of adult males in a particular locality is 70 inches with a standard deviation
of 2.5 inches.
a. If the distribution is normal, the middle 95% of males are between what two heights?
b. Ninety percent of the heights are below what value?
c. Ninety-nine percent of the heights are above what value?
d. What percentage of the heights are between z-scores of ± 1? Of ±2? Of ±3?
Parameters estimation using Normal Distribution
8. Given a normal distribution with a mean of 25, what is the standard deviation if 18% of the values are above
29?
9. Given a normal distribution with a standard deviation of 10, what is the mean if 21% of the values are below
50?
10. Given a normal distribution with 80% of the values above 125 and 90% of the values above 110, what are
the mean and standard deviation?
РЕШЕНИЕ ЭТИХ ЗАДАЧ СМОТРИ В ДОПОЛНИТЕЛЬНОМ МАТЕРИАЛЕ В РАЗДЕЛЕ
«КАЛЬКУЛЯТОРЫ» - Решение задач на нормальное распределение.